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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.

## Docs

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## Tutorials

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## Resources

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