# Linear algebra (numpy.linalg)¶

## Matrix and vector products¶

 dot(a, b) Dot product of two arrays. vdot(a, b) Return the dot product of two vectors. inner(a, b) Inner product of two arrays. outer(a, b) Compute the outer product of two vectors. tensordot(a, b[, axes]) Compute tensor dot product along specified axes for arrays >= 1-D. linalg.matrix_power(M, n) Raise a square matrix to the (integer) power n. kron(a, b) Kronecker product of two arrays.

## Decompositions¶

 linalg.cholesky(a) Cholesky decomposition. linalg.qr(a[, mode]) Compute the qr factorization of a matrix. linalg.svd(a[, full_matrices, compute_uv]) Singular Value Decomposition.

## Matrix eigenvalues¶

 linalg.eig(a) Compute the eigenvalues and right eigenvectors of a square array. linalg.eigh(a[, UPLO]) Return the eigenvalues and eigenvectors of a Hermitian or symmetric matrix. linalg.eigvals(a) Compute the eigenvalues of a general matrix. linalg.eigvalsh(a[, UPLO]) Compute the eigenvalues of a Hermitian or real symmetric matrix.

## Norms and other numbers¶

 linalg.norm(x[, ord]) Matrix or vector norm. linalg.cond(x[, p]) Compute the condition number of a matrix. linalg.det(a) Compute the determinant of an array. trace(a[, offset, axis1, axis2, dtype, out]) Return the sum along diagonals of the array.

## Solving equations and inverting matrices¶

 linalg.solve(a, b) Solve a linear matrix equation, or system of linear scalar equations. linalg.tensorsolve(a, b[, axes]) Solve the tensor equation a x = b for x. linalg.lstsq(a, b[, rcond]) Return the least-squares solution to a linear matrix equation. linalg.inv(a) Compute the (multiplicative) inverse of a matrix. linalg.pinv(a[, rcond]) Compute the (Moore-Penrose) pseudo-inverse of a matrix. linalg.tensorinv(a[, ind]) Compute the ‘inverse’ of an N-dimensional array.

## Exceptions¶

 linalg.LinAlgError Generic Python-exception-derived object raised by linalg functions.