# linalgebra

Version:

Manipulates real and complex matrices.

Balances a matrix to improve the accuracy of eigenvalues and eigenvectors that you compute.
Generates a matrix c with the following structure: c = [ a, 0, ..., 0; 0, b, 0, ...].
Concatenates arrays.
Computes the complex conjugate transpose of a matrix.
Computes the triangular Cholesky factor of a positive definite Hermitian matrix.
Shifts the elements of an array of any dimension in a circular manner.
Returns the condition number of a matrix with the singular value decomposition method.
Returns the eigenvectors, eigenvalues, and condition numbers of all eigenvalues of a matrix.
Returns the companion matrix to a polynomial.
Returns a lower bound for the 1-norm condition number of a square matrix.
Returns an estimate of the reciprocal of the 1-norm condition number of a square matrix.
Removes singleton dimensions from arrays of any dimension.
Computes the determinant of a square matrix.
Computes a diagonal matrix or the diagonal of a matrix.
Computes the eigenvalues and eigenvectors for real or complex square matrices.
Computes eigenvalues and eigenvectors for real or complex square matrices.
Computes the matrix exponential.
Computes the matrix exponential using eigenvectors.
Computes the matrix exponential using the Pade approximation.
Computes the matrix exponential using a Taylor series.
Returns the indexes of all non-zero elements in a matrix.
Performs generalized singular value decomposition (SVD) of a matrix pair.
Converts a matrix to Hessenberg form and returns the unitary transformation matrix.
Concatenates the input arrays horizontally.
Solves the linear equation a x = b in the unknown x.
Computes the matrix logarithm.
Decomposes a matrix into upper and lower triangular or trapezoidal matrices using Gaussian factorization.
Flips an array of any dimension across a specified dimension.
Flips a matrix from left to right.
Flips a matrix from top to bottom.
Computes the norm of a vector or matrix.
Returns the Euclidean norm estimation for a matrix.
Generates an orthonormal basis for the null space of a matrix.
Determines the dimension of an array of any dimension.
Returns the number of elements in an array of any dimension.
Returns the number of non-zero elements in a matrix.
Returns the non-zero elements in a matrix.
Generates an orthonormal basis for the range of a matrix.
Computes the pseudoinverse of a matrix.
Evaluates a polynomial at a matrix value you specify.
Computes the matrix power.
Performs the QR decomposition of an input matrix with or without column pivoting.
Performs the QZ decomposition of a pair of square matrices.
Returns the rank of a matrix.
Changes the dimensions of an input.
Reverses the input array.
Rotates a matrix counterclockwise by a multiple of 90 degrees.
Computes the reduced row echelon form of a matrix with Gaussian elimination using partial pivoting.
Returns the Schur decomposition of a square matrix.
Shifts the dimensions of an array.
Returns the dimensions of an input.
Computes the square root of a square matrix.
Computes the angle between the columns of the input matrices.
Performs singular value decomposition to compute the four fundamental subspaces of a matrix, namely the right and left null spaces and the right and left image spaces.
Computes the sum of all diagonal elements in a matrix.
Computes the non-conjugate transpose of a matrix.
Returns the lower triangular part of a matrix.
Returns the upper triangular part of a matrix.
Performs the Cholesky decomposition on a rank 1 updated or downdated matrix.
Concatenates the input arrays vertically.