Math 2.0

Subjects

15 Linear and multilinear algebra; matrix theory

See MSC 15 on zbMATH Open.

NameTagKindMSC
Vector space000AYPA9AJconcept15A03
Singular value decomposition000NPTMX6Jstatement15A18, 15A23
Block diagonal matrix001T5FJDC1concept15A99
Row equivalence006BHFWMAPconcept15A06
Dimension of the dual space00889YD15Kstatement15A03, 15A04
Linear map of a matrix009892PZ30definition15A04
Scaling a row scales the determinant009CY8JXFXstatement15A15
Composition of linear maps00BKRZKMSSconcept15A04
Lower triangular matrix00J3KZP8Y0concept15A99
Nullity00K4FK4NBHdefinition15A03, 15A04
Determinant00KDZRW4C0concept15A15
Every vector space has a basis00MS9VMQ9Zstatement15A03, 03E25
Positive definite quadratic form00QN1N6MNTdefinition15A63, 11E04
Gram matrix00SPJSDT3Zconcept15A63, 15B57
Linear subspace00YC1D652Kconcept15A03
Jordan–Chevalley decomposition011K11VPJNstatement15A21, 15A20
Leibniz formula for determinants016PE4VZ8Qstatement15A15
Finite-dimensional vector space018W3V3TCTdefinition15A03
Block matrix01AXG9KZQFdefinition15A99
Inner product space01EK923SKPdefinition15A63, 46C05
Determinant of a scalar multiple01EXSMK864statement15A15
Generalised eigenvector01H6QKWGDHconcept15A18
Positive semidefinite matrix01MMVW8CKCconcept15B57, 15A63
Nondegenerate bilinear form01NHFZF2SKconcept15A63
Definite and indefinite quadratic forms01RBSSGMY5concept15A63
Elementary matrix01REXW3WWEconcept15A23
Orthogonal family for a bilinear form01TXN7ETH2concept15A63
Adding a multiple of one row to another preserves the determinant01ZTQBK64Qstatement15A15
Matrix exponential020M04FN1Hconcept15A16
Reflection025158VEYZdefinition15A04, 51F15
Similar matrices027KDW2K72definition15A21
Rank of a product of matrices02FDWY55ASstatement15A03
Polar form of a quadratic form02STTYFBVYdefinition15A63, 11E04
External direct sum02WZB422CEdefinition15A03, 16D10
Kernel of a linear map02YFME3RGWdefinition15A04
Matrix multiplication032Q9FB8MTconcept15A99
Projection033DA1WE8Yconcept15A04
Triangularisation0363JMQ42Ystatement15A20, 15A21
Characteristic polynomial039HF58KQ5definition15A15, 15A18
Column space03AJKXH1AVconcept15A03
Determinant of a linear map03F5KP94K0definition15A04, 15A15
Vector triple product03FTB26QYDstatement15A72
Dimension03GSZ8RTZJconcept15A03
Minimal polynomial03NDVCSHSBconcept15A18
A matrix is invertible iff its determinant is a unit03Q7RE2HXRstatement15A15
Skew-symmetric matrix03RNVFDEANdefinition15A99
Nilpotent matrix0419GJC84Pdefinition15A99
Direct sum of subspaces041JTZCK9Qdefinition15A03
Rational canonical form042JWAR3Q0statement15A21
Multilinear map0443XNARDVconcept15A69
Diagonal matrix044JNC7ZAAconcept15A99
Exponential of a sum of commuting matrices04BD23PSK5statement15A16
Complementary subspaces04C3BAHV03definition15A03
Determinant is multiplicative04CPJ6AF00statement15A15
Spectral theorem for normal matrices04CW1P44VDstatement15A21, 47B15
Coordinate vector04CYQHN6MCconcept15A03
Spectrum of a matrix04EHB7YDQSdefinition15A18
Riesz representation theorem in finite dimensions04GYPXDXNHstatement46C05, 15A04
Consistent and inconsistent systems04JAAVHDDMdefinition15A06
Homogeneous system of linear equations04KGXJG1A2concept15A06
Determinant as signed volume04X3PR72VJconcept15A15
Elementary row operations04XWH28452concept15A06
Product of a matrix and its adjugate0528HKWZ1Zstatement15A09, 15A15
Annihilating polynomial052M4SX57Mdefinition15A18
Eigenvalues are the roots of the characteristic polynomial053QVHF6N7statement15A18
Sesquilinear form054YEQ0Y8Mconcept15A63
A matrix is diagonalisable iff it has a basis of eigenvectors056SW1E0ACstatement15A20
Scalar triple product059Q2XWJDCstatement15A72
Isomorphism with the coordinate space059THXBRBBstatement15A03
Determinant of a family of vectors in a basis05CJSSXPR3concept15A15, 15A75
Vector space05EGHEQZAWdefinition15A03
Polarisation identity05FKHRT0B4statement46C05, 15A63
Dimension05G2G0P224definition15A03
Dot product05HQYM0R4Gdefinition15A63
Matrix of a composition is the product of matrices05Q1B7MH0Mstatement15A04
Orthogonal family for a bilinear form05Q4JD6XEHdefinition15A63
Composition of linear maps05YBKMRVARdefinition15A04
Nilpotent endomorphism063D5Z2C70concept15A04, 15A21
Scalar matrix067NKSBEWTconcept15A99
Row space069MCGX635concept15A03
Laplace expansion along a column06AMCJMMVMstatement15A15
Reflection06BRDF3F0Econcept15A04, 51F15
Identity matrix06DW9BAWB1object15A99
Linear map of a matrix06HMCTAQH3concept15A04
Dimension of a direct product06HN47VPTHstatement15A03
Grassmann's formula06HTJNCMPAstatement15A03
Spectral theorem06J4PXRG22statement47B15, 15A18
Homogeneous system of linear equations06JT7KDHXMdefinition15A06
Every spanning set contains a basis06MRNP4BNTstatement15A03
Dimension of the annihilator06Q1EFVH0Qstatement15A03, 15A04
Rayleigh quotient06WHP8SE98concept15A18, 15A42
Geometric multiplicity06YSJVR356definition15A18
Linear isometry0717XXPWM6definition15A04, 46B04
Associativity of matrix multiplication073E4XC016statement15A99
Symmetric bilinear form0744CN4MDAdefinition15A63
One-sided inverse of a square matrix is two-sided0753Y2X5K6statement15A09
Matrix multiplication076JGP6R3Tdefinition15A99
Determinant of the inverse0783S9D0ZHstatement15A15
Orthogonal complement079D68S3AWdefinition15A63, 46C05
Nilpotent matrix07BSPZPSMFconcept15A99
Signature of a quadratic form07EZA80NEHconcept15A63, 11E04
Circulant matrix07HFRH2AWYexample15B05
Dual space07JBSZE0V4concept15A04
Jordan block07PH4RX0X5concept15A21
Generalised eigenspace07PNDWA7CEdefinition15A18
Trace of a matrix07PTPSZPMEdefinition15A15
Third isomorphism theorem for vector spaces07RB3EMBWWstatement15A03, 16D10
Linear isometry07SJXTWVQWconcept15A04, 46B04
Diagonalisable matrix07SQCNV233concept15A20
Adjugate matrix07W9H8QF38concept15A09, 15A15
Linear form07YQ1C78G0concept15A04
Anticommutativity of the cross product07ZS685JJCstatement15A72
Jordan normal form085HQ5G5TEstatement15A21, 15A20
Positive semidefinite matrix0880F9EQCPdefinition15B57, 15A63
Spanning set088RYKAWK9concept15A03
Existence of an eigenvalue over an algebraically closed field08CJB2NQ92statement15A18
Exterior algebra08HK38GCSMdefinition15A75
Permutation matrix08SP3DF8NBconcept15A99, 05A05
Semisimple endomorphism08VRX3Q4PBconcept15A04, 15A20
Cauchy–Binet formula08WE2W7DYSstatement15A15
Steinitz exchange lemma08ZDRN6H41statement15A03
Alternating bilinear form08ZQAKBKHFdefinition15A63
An injective endomorphism of a finite-dimensional space is surjective0912EEEVCTstatement15A04
Minimal polynomial divides the characteristic polynomial093X6MN6Y6statement15A18
Multiplication by a matrix as a linear map094V2VBJXJconcept15A04
Row equivalence095DDGZF16definition15A06
Linearly independent set of the right size is a basis096V7H13H9statement15A03
Cramer's rule0977KZ6PQBstatement15A06, 15A15
Gauss–Jordan elimination098D6FQN3Nconcept15A06, 65F05
Geometric multiplicity099TWVJ909concept15A18
Transpose09DXWYRD43concept15A99
Coordinates in an orthonormal basis09DZ8CD1AKstatement15A63, 46C05
Trace of a transpose09E1RCZ7YTstatement15A15
Transpose of a product09GK5PS824statement15A99
Scalar multiplication of matrices09V6DDACXRconcept15A99
Singular value09VMDSRXWJconcept15A18
Orthonormal family09VYHEF2VTdefinition15A63, 46C05
Permuting rows multiplies the determinant by the sign09YB3WQG38statement15A15
Determinant of a matrix exponential0A1QQN333Astatement15A16, 15A15
Invariant subspace0ACX5QT8TEconcept15A04, 47A15
Generalised eigenspace0AJ035ZTZEconcept15A18
Multiplication by a matrix as a linear map0AJ0KP1B31definition15A04
Gram matrices are positive semidefinite0AM050KCAWstatement15B57, 15A63
Nullity0APCFW7639concept15A03, 15A04
Second isomorphism theorem for vector spaces0APN65D6Y6statement15A03, 16D10
Unitary matrix0AR68JTMDTconcept15B57, 15A21
Block matrix0ASDFEQS6Pconcept15A99
Annihilator of a subspace0ASHNYF7AGconcept15A04
Back substitution0ATFVE08MWconcept15A06, 65F05
Symmetric bilinear form0AXZNE5XNHconcept15A63
Eigenspace0AYEPBQMAWdefinition15A18
Dual map0AZ5ARP287concept15A04
Eigenvector0B5H4208Z9definition15A18
Orthogonal projection0B8KZRT28Mconcept15A04, 46C05
Linear isomorphism0B8T10CE7Nconcept15A04
Rotation matrix0B9QNFGTHMexample15B10
Matrix determinant lemma0BC3Q6K92Hstatement15A15
Pivot0BCMGDHZGRdefinition15A06
Tensor product of vector spaces0BF2DE2SYKconcept15A69
A linear map is injective iff its kernel is trivial0BJBYCGMWEstatement15A04
Spanning set0BJKVF90Z6definition15A03
Square root of a positive semidefinite matrix0BJVDCF38Yconcept15A16, 15B57
Coordinate vector0BMVBHTWV2definition15A03
Polynomial of an endomorphism0BNEXSKNRVdefinition15A04, 15A54
Eigenvalue0BQAA2BK3Qconcept15A18
Quotient space0BR3FY5Q8Mconcept15A03
Minor0BT9BYWVRYconcept15A15
Matrix addition0BVXADM10Pdefinition15A99
Least squares0BYTQ4X1HCconcept65F20, 15A06
Characteristic polynomial of a linear map0BZ81AJNWFdefinition15A04, 15A18
Laplace expansion along a row0C08BQ3M05statement15A15
Determinant is the product of the eigenvalues0C2F40MEBCstatement15A15, 15A18
Dual map0C2TQMW5A1definition15A04
Determinant0C3CFHDN6Rdefinition15A15
Eigenvalues of a self-adjoint operator are real0C4NT4GT3Xstatement47B15, 15A18
Normal operator0C8BR8XRTRconcept47B15, 15A04
Matrix–vector product0CCQV3884Bdefinition15A99
Classification of complex quadratic forms0CEX9BRXRZstatement11E04, 15A63
Special orthogonal group0CGYNDCWRRobject15B10, 20G20
Equivalent matrices0CMHSGTWXBconcept15A21
Square matrix0CP7YY6NAGdefinition15A99
Linear independence0CRMGPAH83concept15A03
Unitary matrix0D6RMJ10M9definition15B57, 15A21
Matrix of the adjoint is the conjugate transpose0DBTE6HVBDstatement15A04, 47A05
Elementary row operations0DE5R5EB4Ddefinition15A06
Alternating bilinear form0DGDS5XY84concept15A63
Spectral theorem for Hermitian matrices0DGZBQWZWNstatement15A18, 15B57
Linear equation0DNNT7DBFMdefinition15A06
Transvection0DTCBCKEJPconcept15A23
Linear span0DTY8B9HMSconcept15A03
Conjugate transpose0DXKE10PHFconcept15A99, 15B57
Dimension of the orthogonal complement0E2NYPVSP9statement15A03, 46C05
Polynomial of an endomorphism0E3MV6E6MGconcept15A04, 15A54
Algebra of endomorphisms0E3X2G1ZQBobject15A04, 16S50
Similar matrices0E89HQATM8concept15A21
Invertible matrix0EB9N0S33Cconcept15A09
Hermitian matrix0EKZCX4K3Pdefinition15B57
Inverse in terms of the adjugate0ENVM493VKstatement15A09
Normal operator0ENZN5G4CVdefinition47B15, 15A04
Invariant subspace0EP59ESQ94definition15A04, 47A15
Row space0EP73HK4C4definition15A03
Linear subspace0EPTJA5QV4definition15A03
QR decomposition0ERWG4NXQ9statement15A23, 65F25
Gershgorin circle theorem0ETGP0XVCJstatement15A42, 15A18
Linear independence0EVHJFTG9Zdefinition15A03
Rank of a matrix0EWQEYRVA8definition15A03
Conjugate transpose0EX045E2BPdefinition15A99, 15B57
Product of vector spaces0EX2HPXPJ6concept15A03
Lower triangular matrix0EZSD6T9E0definition15A99
Column space0F0RPPJ2TTdefinition15A03
Row echelon form0F27PBRWD7definition15A06
Cayley–Hamilton theorem0F765KFC2Jstatement15A24, 15A18
General linear group0FCHE902D7object20G15, 15A09
Matrix ring0FHVPRAE60object15A99, 16S50
Simultaneous diagonalisation0FK17N4DKAstatement15A20, 15A27
Scalar matrix0FRM62SG7Ddefinition15A99
Trace is a coefficient of the characteristic polynomial0FRYPZ6D0Xstatement15A15, 15A18
Determinant of a matrix with a zero row0FS6B46E5Tstatement15A15
Orthonormal basis0FWJ0VW561definition15A63, 46C05
Algebraic multiplicity0FY42N02DVconcept15A18
Eigenspace0G0RFPG8HRconcept15A18
Sylvester's determinant theorem0G24VQ1088statement15A15
Tensor product of vector spaces0G31VJ5YS5definition15A69
Trace is linear0GJWQZCPZMstatement15A15
Adjugate matrix0GMPYM0NSRdefinition15A09, 15A15
Wedge product of forms0GRAATMGP1concept15A75
System of linear equations0GT4WWGWH2concept15A06
Function space0GZB2SN0PHexample15A03, 46E99
Rule of Sarrus0H8SZFFDXJstatement15A15
Eigenvectors with distinct eigenvalues are linearly independent0HNMFG8F8Kstatement15A18
Coefficient matrix0HQFZAP3NDconcept15A06
Linear span0HR573CHNMdefinition15A03
Rouché–Capelli theorem0HV1SKWPMSstatement15A06
Gram matrix0HX8HZ1WTQdefinition15A63, 15B57
Eigenvalues of a positive definite matrix are positive0HYC2RHD3Mstatement15B57, 15A18
Polar form of a quadratic form0HYFWKKY3Cconcept15A63, 11E04
Quadratic form0HZNE5QZDJdefinition15A63, 11E04
Pivot0J0BBCMJ5Wconcept15A06
Quotient map0J0SK5FF4Mdefinition15A03, 15A04
Polar decomposition0J2C7BDJQAstatement15A23
Characteristic polynomial of a linear map0J5EMJRRFMconcept15A04, 15A18
Endomorphism0J7H0YBFDJconcept15A04
Determinant of a block triangular matrix0J9TVTNB4Kstatement15A15
Image of a linear map0JB228DCWBdefinition15A04
Linear combination0JB3DP1BMFdefinition15A03
Rank of a linear map0JGB7A6GTSdefinition15A03, 15A04
Space of polynomials of bounded degree0JGZCDT5DNexample15A03
Eigenspaces of a self-adjoint operator are orthogonal0JHGAV9H25statement47B15, 15A18
Kronecker product0JK6M18QZHdefinition15A69
Sum of subspaces0JMTY8MF54concept15A03
System of linear equations0JTRMBQ1SAdefinition15A06
Gaussian elimination0JVJ2WCXZHconcept15A06, 65F05
An orthonormal family is linearly independent0JWM6GJNQWstatement15A63, 46C05
Square matrix0JXZKX526Rconcept15A99
Determinant of a triangular matrix0K1KKMFHYHstatement15A15
Scalar multiplication of matrices0K28YXMS7Qdefinition15A99
Singular value0K2TX12X58definition15A18
Determinant of a matrix with two equal rows0K4VQB7HWRstatement15A15
Rayleigh quotient0K4WCNTMHGdefinition15A18, 15A42
Matrix exponential0K665H5V1Sdefinition15A16
Alternating multilinear map0K6CH0MT0Fconcept15A69, 15A75
Idempotent matrix0K7TD9BV2Ddefinition15A99
Determinant via the Schur complement0KA7A4ENVJstatement15A15
Nondegenerate bilinear form0KAN330PAHdefinition15A63
Idempotent matrix0KCE8CG86Pconcept15A99
Basis0KCQ9Y3QKAconcept15A03
Determinant of a linear map is the determinant of its matrix0KMN32XGPFstatement15A04, 15A15
Restriction of an endomorphism to an invariant subspace0KN7EPH7Z0concept15A04, 47A15
Signature of a quadratic form0KQZYGEJTFdefinition15A63, 11E04
Symmetric bilinear form associated with a quadratic form0KRVRV5V80concept15A63, 11E04
Change of basis matrix0KWXYZPJKNdefinition15A03, 15A04
Positive definite matrix0KX66CZMBBconcept15B57, 15A63
Trace of a linear map0KZDNGA561concept15A04, 15A15
Block diagonal matrix0M0SNKZ482definition15A99
Every linearly independent set extends to a basis0M4SXE5WW3statement15A03
Elementary matrix0M79HRJCRRdefinition15A23
Complementary subspaces0M83V17KHXconcept15A03
Dual space0M856Q1AMZdefinition15A04
Nilpotent endomorphism0M8MHYERTYdefinition15A04, 15A21
Self-adjoint operator0MB8HQW495definition47B15, 15B57
Exterior algebra0MDMZ965VEconcept15A75
Upper triangular matrix0MKABWDRNCdefinition15A99
Change of basis matrix0MKRHZB3WSconcept15A03, 15A04
Product of vector spaces0MM085RX00definition15A03
Diagonalisable iff the minimal polynomial has distinct roots0MPAJRB23Tstatement15A20
Change of basis formula0MQXVZEBMTstatement15A04
Normal matrix0MR0BYF0K2concept15B57, 15A21
Alternating multilinear map0MSWYWHYF5definition15A69, 15A75
First isomorphism theorem for linear maps0MTBGVZ4XJstatement15A04, 16D10
Matrix0N1MY1T0W9definition15A99
Symmetric matrix0N28QN4CYAdefinition15A99, 15B57
Quotient map0N4F5FMQZWconcept15A03, 15A04
Upper triangular matrix0N4XY7Z3NNconcept15A99
Square root of a positive semidefinite matrix0N5GP3YT8Tdefinition15A16, 15B57
Cross product0N5N15HWZ7concept15A72
Eigenvector0N6960W0BVconcept15A18
Kronecker product0N7ENQRCXNconcept15A69
Inner product0NB0AWGJBWconcept15A63, 46C05
Self-adjoint operator0NEGN5CRSCconcept47B15, 15B57
Transvection0NMN00FNW1definition15A23
Trace is the sum of the eigenvalues0NMXDCNNKRstatement15A15, 15A18
Reduced row echelon form0NNR68BFRYdefinition15A06
Linear map0NRYHJPQG2concept15A04
Hermitian matrix0P17NGQQMQconcept15B57
Equivalent matrices0P21AVFFSPdefinition15A21
Matrix of a bilinear form0P24YW565Fdefinition15A63
Non-commutativity of matrix multiplication0P506SPZP2counterexample15A27
Bilinear form0P799D6AMNdefinition15A63
Coefficient matrix0P7A2MJD24definition15A06
Vandermonde determinant0P84B554ASstatement15A15, 15B05
Existence of a complementary subspace0P9T8WHNMHstatement15A03
Jordan block0PBFS92AJPdefinition15A21
Annihilating polynomial0PBN8VEKY8concept15A18
Skew-symmetric matrix0PBY4E9GQFconcept15A99
Matrix–vector product0PDVQEP0ZCconcept15A99
Restriction of an endomorphism to an invariant subspace0PFPWKBDTJdefinition15A04, 47A15
Null space0PHDYNR24Dconcept15A03, 15A06
Determinant is multilinear in the rows0PPG793642statement15A15
Null space0PQ2GGY1QVdefinition15A03, 15A06
Principal axis theorem0PR5P9Z4KMstatement15A63, 15A18
Moore–Penrose inverse0PSRCMCM5Xdefinition15A09
Endomorphism0PTF1PTJK0definition15A04
Linear equation0Q3ZT8J05Rconcept15A06
Permutation matrix0Q5SM60HTHdefinition15A99, 05A05
Orientation of a real vector space0Q8BZXVT1Zdefinition15A04, 15A15
Orthogonal projection0Q8HZTJC7Gdefinition15A04, 46C05
Diagonal matrix0Q9PGXD9E4definition15A99
Cayley–Hamilton theorem for linear maps0QEM68Y0DEstatement15A04, 15A18
Eigenvalues are the roots of the minimal polynomial0QF4ZEFG52statement15A18
Orientation of a real vector space0QJJAQ6ZYZconcept15A04, 15A15
Matrix of a bilinear form0QK6K857HSconcept15A63
Dimension of the coordinate space0QK7FPE6VEstatement15A03
Positive definite matrix0QQCG3JWJ4definition15B57, 15A63
Orthogonal matrix0QRBVFJ50Xdefinition15B10
Semisimple endomorphism0QS8P74F2Zdefinition15A04, 15A20
Inner product space0QVNCJXRY3concept15A63, 46C05
Dimension of a subspace0QW084460Estatement15A03
Annihilator of a subspace0R6M158SQ9definition15A04
A linear isometry preserves the inner product0R7VXTYHYZstatement15A04, 46C05
Dimension of a tensor product0R84PF4JV7statement15A69, 15A03
A linear map is determined by its values on a basis0R8X9XA83Astatement15A04
Adjoint of a linear map0R9NMSM1ZPconcept15A04, 47A05
Unitary group0R9R0Y1HDKobject15B57, 20G20
Quadratic form0RBQS1JJCRconcept15A63, 11E04
Space of matrices0RE6X3BGPNexample15A03
Cauchy–Schwarz inequality0RFWW56Y22statement15A63, 46C05
Projection0RH4E3CAV9definition15A04
Linear map0RJF668P1Tdefinition15A04
LU decomposition0RKG5YW66Yconcept15A23, 65F05
Sum of subspaces0RMKABS2S5definition15A03
Positive definite quadratic form0RP20HFYM3concept15A63, 11E04
Trace of a linear map0RPDTWY2JSdefinition15A04, 15A15
Linear form0RT96J4D3Hdefinition15A04
Orthonormal family0RW9TNNT87concept15A63, 46C05
Distributivity of matrix multiplication0RXD6EZYBKstatement15A99
Wedge product of forms0S166D363Mdefinition15A75
Kernel of a linear map0S23E6YE83concept15A04
Inverse of a product0S4WTRE9GGstatement15A09
Dot product0S52TNNTH9concept15A63
Algebraic multiplicity0S7A0EMPF4definition15A18
External direct sum0S7W6EG32Vconcept15A03, 16D10
Orthonormal basis0S9GGTR0EXconcept15A63, 46C05
Generalised eigenvector0SAAHC36J9definition15A18
Minor0SD528P0EKdefinition15A15
Multilinear map0SDMPMCN43definition15A69
Cross product0SEDGXG9S3definition15A72
Basis of a tensor product0SH5VT8QYAstatement15A69
Change of basis for a bilinear form0SPYAGE7T0statement15A63, 15A21
Bilinear form0SQZMXB6GPconcept15A63
Differentiation as a linear map0SS770NS8Bexample15A04, 12E10
Adjoint of a linear map0ST8QF9T3Tdefinition15A04, 47A05
Quotient space0SVR29SV1Vdefinition15A03
Dimension of a quotient space0SXDQ6TN00statement15A03
Determinant is a coefficient of the characteristic polynomial0T0X8GTYYSstatement15A15, 15A18
The cross product is perpendicular to its factors0T4QHJXSD4statement15A72
Augmented matrix0T6MWGZSXAconcept15A06
Orthogonal group0TKYAEJ8N7object15B10, 20G20
Powers of a diagonalisable matrix0TNR9BQ871concept15A20, 15A16
Orthogonal vectors0TS7VZJBWDdefinition15A63, 46C05
Invertible matrix0TWTS88TWNdefinition15A09
Symmetric bilinear form associated with a quadratic form0TX2YH2FQSdefinition15A63, 11E04
Characteristic polynomial does not depend on the basis0TYMASG33Ystatement15A15, 15A18
Row rank equals column rank0TZAG60ZYTstatement15A03
Intersection of subspaces0V33SPH7RRstatement15A03
Minimal polynomial0V58FPM3EQdefinition15A18
Standard basis0V7ZD6P7RKobject15A03
Linear combination0V8F3E48E6concept15A03
Determinant of a family of vectors in a basis0V94H674MBdefinition15A15, 15A75
Special linear group0V9PMN0RBHobject15A15, 20G15
Matrix0VD9ZSWWJGconcept15A99
Inner product0VGSYBWHV2definition15A63, 46C05
Companion matrix0VH1TC1PWFdefinition15A21
Finite-dimensional spaces are isomorphic iff they have equal dimension0VJBSK15SNstatement15A03
Cartan–Dieudonné theorem0VMWGYY35Qstatement51F15, 15B10
Space of linear maps0VPCJWGMP9definition15A04
Symmetric matrix0VR671PHE5concept15A99, 15B57
Characteristic polynomial0VSSPAFM2Cconcept15A15, 15A18
Gram–Schmidt process0VT6P0GNQRconcept15A63, 65F25
Minimal polynomial divides every annihilating polynomial0VTAD25A3Gstatement15A18
Basis0VTQTPQGAVdefinition15A03
Row echelon form0VYCDGMJJJconcept15A06
Orthogonal matrix0W02QESPJQconcept15B10
Cofactor0W2QAVJQ1Wdefinition15A15
Sesquilinear form0W44K2VNBDdefinition15A63
Rank–nullity theorem0W4FSW1TVBstatement15A03, 15A04
Dual basis0W6M3PSD08definition15A04
Transpose0W809K6AW0definition15A99
Trace of a linear map is the trace of its matrix0WCPH5Z7FAstatement15A04, 15A15
Reduced row echelon form0WF5AQYTW6concept15A06
Sylvester's law of inertia0WFED3K3DQstatement15A63, 11E04
A subspace of full dimension is the whole space0WGAXEK99Estatement15A03
Dimension theorem for vector spaces0WK0Y8RH1Mstatement15A03
Sylvester's criterion0WKEF78PMVstatement15B57, 15A15
Cholesky decomposition0WKG8CYY6Astatement15A23, 65F05
Image of a linear map0WSFKKT6FFconcept15A04
Gram–Schmidt vectors are orthogonal0WXBGBTA3Dstatement15A63, 65F25
Determinant of a linear map0X0HQYSZ0Kconcept15A04, 15A15
Consistent and inconsistent systems0X6V9B1V10concept15A06
Space of linear maps0X9MBPP2Z3concept15A04
Trace of a matrix0XC1RDBY7Aconcept15A15
Orthogonal complement0XJXTBCB2Tconcept15A63, 46C05
Coordinate space0XM8BZD76Gobject15A03
Cofactor0XPKR18APAconcept15A15
Spectrum of a matrix0XPX5NC67Econcept15A18
Linear isomorphism0XSJ25Z9M4definition15A04
Normal matrix0XYKE8BE7Xdefinition15B57, 15A21
Direct sum of subspaces0XYYT5KNTXconcept15A03
Diagonalisable matrix0Y17PEKF24definition15A20
Orthogonal vectors0Y2X7P2WB7concept15A63, 46C05
Trace of a product is symmetric0Y4NF1DRKDstatement15A15
Matrix addition0Y7H3SAVA1concept15A99
Existence of an orthonormal basis0Y85GYEGSFstatement15A63, 46C05
Distinct eigenvalues imply diagonalisable0Y95Z7MT02statement15A20
Matrix exponential as the solution of a linear system0YC8JT513Jstatement34A30, 15A16
Augmented matrix0YCDZ7N8VDdefinition15A06
Universal property of the tensor product0YDRV01R8Fstatement15A69
Matrix of a linear map0YQSGNYE3Kconcept15A04
Moore–Penrose inverse0YY8VX28JRconcept15A09
Matrix of a linear map0YYMY95FWSdefinition15A04
Determinant as a group homomorphism0YZ3T5Q7XNexample15A15
Diagonalisation of a quadratic form0Z3FEWZ8HAstatement11E04, 15A63
Decomposition into generalised eigenspaces0Z3GDY89T5statement15A18, 15A21
Determinant of the identity matrix0Z4BWARC38statement15A15
Computing the inverse by row reduction0Z83DHFMYMconcept15A09, 65F05
Dimension of the space of linear maps0Z9N1ER0W0statement15A03, 15A04
Rank of a matrix0ZC9YTXZRYconcept15A03
Companion matrix0ZCWPNZTQ3concept15A21
Dual basis0ZD2CF6ZS0concept15A04
Universal property of the quotient space0ZERJX6PH6statement15A04
Finite-dimensional vector space0ZHWKQMVX5concept15A03
Canonical isomorphism with the double dual0ZJM9D7NPSstatement15A04
Determinant of a 2 by 2 matrix0ZN2J42SK7statement15A15
Eigenvalue0ZND7NQ970definition15A18
Matrix of the dual map is the transpose0ZPB3180AYstatement15A04
Zero matrix0ZTKJJDGR7object15A99
Determinant of a transpose0ZZQ2E1MTEstatement15A15
Rank of a linear map0ZZXSBTR4Jconcept15A03, 15A04