https://docs.scipy.org/doc/numpy/reference/routines.linalg.html
矩阵与向量乘积
| 方法 | 描述 |
|---|---|
| dot(a, b[, out]) | Dot product of two arrays. |
| linalg.multi_dot(arrays) | Compute the dot product of two or more arrays in a single function call, while automatically selecting the fastest evaluation order. |
| vdot(a, b) | Return the dot product of two vectors. |
| inner(a, b) | Inner product of two arrays. |
| outer(a, b[, out]) | Compute the outer product of two vectors. |
| matmul(a, b[, out]) | Matrix product of two arrays. |
| tensordot(a, b[, axes]) | Compute tensor dot product along specified axes for arrays >= 1-D. |
| einsum(subscripts, *operands[, out, dtype, …]) | Evaluates the Einstein summation convention on the operands. |
| einsum_path(subscripts, *operands[, optimize]) | Evaluates the lowest cost contraction order for an einsum expression by considering the creation of intermediate arrays. |
| linalg.matrix_power(M, n) | Raise a square matrix to the (integer) power n. |
| kron(a, b) | Kronecker product of two arrays. |
分解
| 方法 | 描述 |
|---|---|
| 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. |
特征值特征向量
| 方法 | 描述 |
|---|---|
| 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
| 方法 | 描述 |
|---|---|
| linalg.norm(x[, ord, axis, keepdims]) | 求范数， 默认是二范数 |
| linalg.cond(x[, p]) | Compute the condition number of a matrix. |
| linalg.det(a) | Compute the determinant of an array. |
| linalg.matrix_rank(M[, tol, hermitian]) | Return matrix rank of array using SVD method |
| linalg.slogdet(a) | Compute the sign and (natural) logarithm of 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
| 方法 | 描述 |
|---|---|
| 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
| 方法 | 描述 |
|---|---|
| linalg.LinAlgError | Generic Python-exception-derived object raised by linalg functions. |