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# torch.linalg¶

Common linear algebra operations.

See Linear algebra (torch.linalg) for some common numerical edge-cases.

## Matrix Properties¶

 norm Computes a vector or matrix norm. vector_norm Computes a vector norm. matrix_norm Computes a matrix norm. diagonal Alias for torch.diagonal() with defaults dim1= -2, dim2= -1. 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. lu Computes the LU decomposition with partial pivoting of a matrix. lu_factor Computes a compact representation of the LU factorization with partial pivoting 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. solve_triangular Computes the solution of a triangular system of linear equations with a unique solution. lu_solve Computes the solution of a square system of linear equations with a unique solution given an LU decomposition. 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 Functions¶

 matrix_exp Computes the matrix exponential of a square matrix. matrix_power Computes the n-th power of a square matrix for an integer n.

## Matrix Products¶

 cross Computes the cross product of two 3-dimensional vectors. matmul Alias for torch.matmul() vecdot Computes the dot product of two batches of vectors along a dimension. 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.

## Misc¶

 vander Generates a Vandermonde matrix.

## 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. solve_ex A version of solve() that does not perform error checks unless check_errors= True. lu_factor_ex This is a version of lu_factor() that does not perform error checks unless check_errors= True. ldl_factor Computes a compact representation of the LDL factorization of a Hermitian or symmetric (possibly indefinite) matrix. ldl_factor_ex This is a version of ldl_factor() that does not perform error checks unless check_errors= True. ldl_solve Computes the solution of a system of linear equations using the LDL factorization.

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