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# Linear algebra (`scipy.linalg`)

## Basics

`inv` (a[, overwrite_a]) | Compute the inverse of a matrix.
`solve` (a, b[, sym_pos, lower, ...]) | Solve the equation a x = b for x
`solve_banded` ((l, u), ab, b[, overwrite_ab, overwrite_b, ...]) | Solve the equation a x = b for x, assuming a is banded matrix.
`solveh_banded` (ab, b[, overwrite_ab, overwrite_b, ...]) | Solve equation a x = b. a is Hermitian positive-definite banded matrix.
`det` (a[, overwrite_a]) | Compute the determinant of a matrix
`norm` (x[, ord]) | Matrix or vector norm.
`lstsq` (a, b[, cond, overwrite_a, ...]) | Compute least-squares solution to equation :m:`a x = b`
`pinv` (a[, cond, rcond]) | Compute the (Moore-Penrose) pseudo-inverse of a matrix.
`pinv2` (a[, cond, rcond]) | Compute the (Moore-Penrose) pseudo-inverse of a matrix.

## Eigenvalues and Decompositions

`eig` (a[, b, left, right, ...]) | Solve an ordinary or generalized eigenvalue problem of a square matrix.
`eigvals` (a[, b, overwrite_a]) | Compute eigenvalues from an ordinary or generalized eigenvalue problem.
`eigh` (a[, b, lower, eigvals_only, ...]) | Solve an ordinary or generalized eigenvalue problem for a complex Hermitian or real symmetric matrix.
`eigvalsh` (a[, b, lower, overwrite_a, ...]) | Solve an ordinary or generalized eigenvalue problem for a complex Hermitian or real symmetric matrix.
`eig_banded` (a_band[, lower, eigvals_only, ...]) | Solve real symmetric or complex hermetian band matrix eigenvalue problem.
`eigvals_banded` (a_band[, lower, overwrite_a_band, ...]) | Solve real symmetric or complex hermitian band matrix eigenvalue problem.
`lu` (a[, permute_l, overwrite_a]) | Compute pivoted LU decompostion of a matrix.
`lu_factor` (a[, overwrite_a]) | Compute pivoted LU decomposition of a matrix.
`lu_solve` ((lu, piv), b[, trans, overwrite_b]) | Solve an equation system, a x = b, given the LU factorization of a
`svd` (a[, full_matrices, compute_uv, ...]) | Singular Value Decomposition.
`svdvals` (a[, overwrite_a]) | Compute singular values of a matrix.
`diagsvd` (s, M, N) | Construct the sigma matrix in SVD from singular values and size M,N.
`orth` (A) | Construct an orthonormal basis for the range of A using SVD
`cholesky` (a[, lower, overwrite_a]) | Compute the Cholesky decomposition of a matrix.
`cholesky_banded` (ab[, overwrite_ab, lower]) | Cholesky decompose a banded Hermitian positive-definite matrix
`cho_factor` (a[, lower, overwrite_a]) | Compute the Cholesky decomposition of a matrix, to use in cho_solve
`cho_solve` (clow, b) | Solve a previously factored symmetric system of equations.
`qr` (a[, overwrite_a, lwork, ...]) | Compute QR decomposition of a matrix.
`schur` (a[, output, lwork, overwrite_a]) | Compute Schur decomposition of a matrix.
`rsf2csf` (T, Z) | Convert real Schur form to complex Schur form.
`hessenberg` (a[, calc_q, overwrite_a]) | Compute Hessenberg form of a matrix.

## Matrix Functions

`expm` (A[, q]) | Compute the matrix exponential using Pade approximation.
`expm2` (A) | Compute the matrix exponential using eigenvalue decomposition.
`expm3` (A[, q]) | Compute the matrix exponential using Taylor series.
`logm` (A[, disp]) | Compute matrix logarithm.
`cosm` (A) | Compute the matrix cosine.
`sinm` (A) | Compute the matrix sine.
`tanm` (A) | Compute the matrix tangent.
`coshm` (A) | Compute the hyperbolic matrix cosine.
`sinhm` (A) | Compute the hyperbolic matrix sine.
`tanhm` (A) | Compute the hyperbolic matrix tangent.
`signm` (a[, disp]) | Matrix sign function.
`sqrtm` (A[, disp]) | Matrix square root.
`funm` (A, func[, disp]) | Evaluate a matrix function specified by a callable.

## Iterative linear systems solutions

`cg` (*args, **kwds) | scipy.linalg.cg is DEPRECATED!! – use scipy.sparse.linalg.cg instead
`cgs` (*args, **kwds) | scipy.linalg.cgs is DEPRECATED!! – use scipy.sparse.linalg.cgs instead
`qmr` (*args, **kwds) | scipy.linalg.qmr is DEPRECATED!! – use scipy.sparse.linalg.qmr instead
`gmres` (*args, **kwds) | scipy.linalg.gmres is DEPRECATED!! – use scipy.sparse.linalg.gmres instead
`bicg` (*args, **kwds) | scipy.linalg.bicg is DEPRECATED!! – use scipy.sparse.linalg.bicg instead
`bicgstab` (*args, **kwds) | scipy.linalg.bicgstab is DEPRECATED!! – use scipy.sparse.linalg.bicgstab instead

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