Arithmetic

· 5

+

Matrix addition

−

Matrix subtraction

k

Multiplying a matrix by a number

×

Matrix multiplication

Aⁿ

Power of a matrix

Properties

· 6

det

Matrix determinant

Cofactor expansionSarrusTriangular FormMontante

A⁻¹

Matrix inverse

Gauss-JordanAdjugate matrixGaussian eliminationMontante

Mᵢⱼ

Matrix minor

Cᵢⱼ

Matrix cofactor

adj

Adjugate matrix

r

Rank of matrix

Elementary transformationsBordering minors

Transformations

· 3

Aᵀ

Transpose matrix

Ā

Conjugate matrix

√A

Square root

Equations

· 2

AX

Matrix equations

{

System of linear equations

Gaussian eliminationCramer's ruleGauss-JordanInverse matrix methodMontante

Eigen

· 2

λ

Eigenvalues

v

Eigenvectors

Decompositions

· 7

LU

LU decomposition

QR

QR decomposition

Gram–SchmidtHouseholder reflectionsGivens rotation

LL

Cholesky decomposition

QT

Schur Decomposition

PDP

Eigendecomposition(matrix diagonalization)

QH

Polar decomposition

σ

Singular Value Decomposition

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