Matrix Math and Special Matrices

 

{ } Array Construction

Create a series or multiple column array

*^ (Matrix Multiply)

Multiply two matrices

\^ (Matrix Solve)

Matrix solve

/^ (Matrix Right Division)

Matrix right division

^^ (Matrix Power)

Raise a matrix to a power

' (Matrix Transpose)

Swap the rows and columns of a specified table

~^ (Conjugate Transpose)

Complex conjugate transpose

BALANCE

Balance a matrix

CHOLESKY

Compute the Cholesky factorization of a square matrix

COLNOS

Return an array of COL numbers

COND

Estimate the condition number of a matrix

CROSSPROD

Calculate the matrix cross product

DET

Calculate matrix determinant

DIAGONAL

Get the main diagonal of a matrix

EIG

Compute the eigenvalues and eigenvectors of a square matrix

EIGVAL

Get eigenvalues of a matrix

EIGVEC

Get eigenvectors of a matrix

EXPM

Calculate the exponential of a matrix

FUNM

Calculate a general matrix function

HANKEL

Generate a Hankel matrix

HESS

Find the Hessenberg form of a matrix

INNERPROD

Matrix Inner Product

INTERPOSE

Apply REDUCE associatively

INVERSE

Invert a matrix

KRON

Compute the Kronecker tensor product

LLU

Lower triangular matrix in LU decomposition

LOGM

Calculate the matrix log

LOTRI

Return the lower triangle of a matrix including the main diagonal

LOTRIX

Return the lower triangle of a matrix excluding the main diagonal

LU

LU decomposition

MDIV

Matrix solve

MMULT

Matrix multiplication

NBEIGVAL

Get eigenvalues without balancing step

NBEIGVEC

Get eigenvectors without balancing step

NORM

Calculate the norm of a series or array

NULL

Compute an orthogonal basis for the Null space of an array

ORTH

Compute an orthonormal basis of an array using SVD

OUTERPROD

Outer product of two vectors

PARTPROD

Partial product of two vectors

PINV

Calculate the pseudo inverse of a matrix using SVD

QR

QR decomposition

RANK

Estimate the number of independent rows or columns of an array

RCOND

Estimate the reciprocal condition number

ROWNOS

Return an array of row numbers

SCHUR

Generate the SCHUR form of a matrix

SIZE

Return a 2 point series containing the dimensions of an array

SQRTM

Calculate the matrix square root

SVD

Singular value decomposition

TOEPLITZ

Generate a Toeplitz matrix

TRACE

Calculate the trace of an array, the sum of the diagonal elements

TRANSPOSE

Transpose a matrix

TRANSPOSECONJ

Conjugate transpose a matrix

ULU

Upper triangular matrix in LU decomposition

UPTRI

Return the upper triangle of a matrix including the main diagonal

UPTRIX

Return the upper triangle of a matrix excluding the main diagonal

USCHUR

Compute the SCHUR form of an input matrix

VANDER

Generate a Vandermonde matrix