# torch.linalg¶

Common linear algebra operations.

## Matrix Properties¶

 norm Computes a vector or matrix norm. vector_norm Computes a vector norm. matrix_norm Computes a matrix norm. det Computes the determinant of a square matrix. slogdet Computes the sign and natural logarithm of the absolute value of the determinant of a square matrix. cond Computes the condition number of a matrix with respect to a matrix norm. matrix_rank Computes the numerical rank of a matrix.

## Decompositions¶

 cholesky Computes the Cholesky decomposition of a complex Hermitian or real symmetric positive-definite matrix. qr Computes the QR decomposition of a matrix. eig Computes the eigenvalue decomposition of a square matrix if it exists. eigvals Computes the eigenvalues of a square matrix. eigh Computes the eigenvalue decomposition of a complex Hermitian or real symmetric matrix. eigvalsh Computes the eigenvalues of a complex Hermitian or real symmetric matrix. svd Computes the singular value decomposition (SVD) of a matrix. svdvals Computes the singular values of a matrix.

## Solvers¶

 solve Computes the solution of a square system of linear equations with a unique solution. lstsq Computes a solution to the least squares problem of a system of linear equations.

## Inverses¶

 inv Computes the inverse of a square matrix if it exists. pinv Computes the pseudoinverse (Moore-Penrose inverse) of a matrix.

## Matrix Products¶

 matrix_power Computes the n-th power of a square matrix for an integer n. multi_dot Efficiently multiplies two or more matrices by reordering the multiplications so that the fewest arithmetic operations are performed. householder_product Computes the first n columns of a product of Householder matrices.

## Tensor Operations¶

 tensorinv Computes the multiplicative inverse of torch.tensordot(). tensorsolve Computes the solution X to the system torch.tensordot(A, X) = B.

## Experimental Functions¶

 cholesky_ex Computes the Cholesky decomposition of a complex Hermitian or real symmetric positive-definite matrix. inv_ex Computes the inverse of a square matrix if it is invertible.