（翻译英文）线性代数

Author: lisniuse

docs/reference/routines/linalg.md

@@ -1,91 +1,80 @@
-# Linear algebra (``numpy.linalg``)
+# 线性代数（``numpy.linalg``）
 
-The NumPy linear algebra functions rely on BLAS and LAPACK to provide efficient
-low level implementations of standard linear algebra algorithms. Those
-libraries may be provided by NumPy itself using C versions of a subset of their
-reference implementations but, when possible, highly optimized libraries that
-take advantage of specialized processor functionality are preferred. Examples
-of such libraries are [OpenBLAS](https://www.openblas.net/), MKL (TM), and ATLAS. Because those libraries
-are multithreaded and processor dependent, environmental variables and external
-packages such as [threadpoolctl](https://github.com/joblib/threadpoolctl) may be needed to control the number of threads
-or specify the processor architecture.
+NumPy线性代数函数依赖于BLAS和LAPACK来提供标准线性代数算法的高效低级实现。
+这些库可以由NumPy本身使用其参考实现子集的C版本提供，
+但如果可能，最好是利用专用处理器功能的高度优化的库。
+这样的库的例子是[OpenBLAS](https://www.openblas.net/)、MKL(TM)和ATLAS。因为这些库是多线程和处理器相关的，
+所以可能需要环境变量和外部包（如[threadpoolctl](https://github.com/joblib/threadpoolctl)）来控制线程数量或指定处理器体系结构。
 
-## Matrix and vector products
+## 矩阵和向量积
 
-method | description
+方法 | 描述
 ---|---
-[dot](https://numpy.org/devdocs/reference/generated/numpy.dot.html#numpy.dot)(a, b[, out]) | Dot product of two arrays.
-[linalg.multi_dot](https://numpy.org/devdocs/reference/generated/numpy.linalg.multi_dot.html#numpy.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](https://numpy.org/devdocs/reference/generated/numpy.vdot.html#numpy.vdot)(a, b) | Return the dot product of two vectors.
-[inner](https://numpy.org/devdocs/reference/generated/numpy.inner.html#numpy.inner)(a, b) | Inner product of two arrays.
-[outer](https://numpy.org/devdocs/reference/generated/numpy.outer.html#numpy.outer)(a, b[, out]) | Compute the outer product of two vectors.
-[matmul](https://numpy.org/devdocs/reference/generated/numpy.matmul.html#numpy.matmul)(x1, x2, /[, out, casting, order, …]) | Matrix product of two arrays.
-[tensordot](https://numpy.org/devdocs/reference/generated/numpy.tensordot.html#numpy.tensordot)(a, b[, axes]) | Compute tensor dot product along specified axes.
-[einsum](https://numpy.org/devdocs/reference/generated/numpy.einsum.html#numpy.einsum)(subscripts, *operands[, out, dtype, …]) | Evaluates the Einstein summation convention on the operands.
-[einsum_path](https://numpy.org/devdocs/reference/generated/numpy.einsum_path.html#numpy.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](https://numpy.org/devdocs/reference/generated/numpy.linalg.matrix_power.html#numpy.linalg.matrix_power)(a, n) | Raise a square matrix to the (integer) power n.
-[kron](https://numpy.org/devdocs/reference/generated/numpy.kron.html#numpy.kron)(a, b) | Kronecker product of two arrays.
-
-## Decompositions
-
-method | description
+[dot](https://numpy.org/devdocs/reference/generated/numpy.dot.html#numpy.dot)(a, b[, out]) | 两个数组的点积。
+[linalg.multi_dot](https://numpy.org/devdocs/reference/generated/numpy.linalg.multi_dot.html#numpy.linalg.multi_dot)(arrays) | 在单个函数调用中计算两个或更多数组的点积，同时自动选择最快的求值顺序。
+[vdot](https://numpy.org/devdocs/reference/generated/numpy.vdot.html#numpy.vdot)(a, b) | 返回两个向量的点积。
+[inner](https://numpy.org/devdocs/reference/generated/numpy.inner.html#numpy.inner)(a, b) | 两个数组的内积。
+[outer](https://numpy.org/devdocs/reference/generated/numpy.outer.html#numpy.outer)(a, b[, out]) | 计算两个向量的外积。
+[matmul](https://numpy.org/devdocs/reference/generated/numpy.matmul.html#numpy.matmul)(x1, x2, /[, out, casting, order, …]) | 两个数组的矩阵乘积。
+[tensordot](https://numpy.org/devdocs/reference/generated/numpy.tensordot.html#numpy.tensordot)(a, b[, axes]) | 沿指定轴计算张量点积。
+[einsum](https://numpy.org/devdocs/reference/generated/numpy.einsum.html#numpy.einsum)(subscripts, *operands[, out, dtype, …]) | 计算操作数上的爱因斯坦求和约定。
+[einsum_path](https://numpy.org/devdocs/reference/generated/numpy.einsum_path.html#numpy.einsum_path)(subscripts, *operands[, optimize]) | 通过考虑中间数组的创建，计算einsum表达式的最低成本压缩顺序。
+[linalg.matrix_power](https://numpy.org/devdocs/reference/generated/numpy.linalg.matrix_power.html#numpy.linalg.matrix_power)(a, n) | 将方阵提升为(整数)n次方。
+[kron](https://numpy.org/devdocs/reference/generated/numpy.kron.html#numpy.kron)(a, b) | 两个数组的Kronecker乘积。
+
+## 分解
+
+方法 | 描述
 ---|---
-[linalg.cholesky](https://numpy.org/devdocs/reference/generated/numpy.linalg.cholesky.html#numpy.linalg.cholesky)(a) | Cholesky decomposition.
-[linalg.qr](https://numpy.org/devdocs/reference/generated/numpy.linalg.qr.html#numpy.linalg.qr)(a[, mode]) | Compute the qr factorization of a matrix.
-[linalg.svd](https://numpy.org/devdocs/reference/generated/numpy.linalg.svd.html#numpy.linalg.svd)(a[, full_matrices, compute_uv, …]) | Singular Value Decomposition.
+[linalg.cholesky](https://numpy.org/devdocs/reference/generated/numpy.linalg.cholesky.html#numpy.linalg.cholesky)(a) | Cholesky分解
+[linalg.qr](https://numpy.org/devdocs/reference/generated/numpy.linalg.qr.html#numpy.linalg.qr)(a[, mode]) | 计算矩阵的QR分解。
+[linalg.svd](https://numpy.org/devdocs/reference/generated/numpy.linalg.svd.html#numpy.linalg.svd)(a[, full_matrices, compute_uv, …]) | 奇异值分解
 
-## Matrix eigenvalues
+## 矩阵特征值
 
-method | description
+方法 | 描述
 ---|---
-[linalg.eig](https://numpy.org/devdocs/reference/generated/numpy.linalg.eig.html#numpy.linalg.eig)(a) | Compute the eigenvalues and right eigenvectors of a square array.
-[linalg.eigh](https://numpy.org/devdocs/reference/generated/numpy.linalg.eigh.html#numpy.linalg.eigh)(a[, UPLO]) | Return the eigenvalues and eigenvectors of a complex Hermitian (conjugate symmetric) or a real symmetric matrix.
-[linalg.eigvals](https://numpy.org/devdocs/reference/generated/numpy.linalg.eigvals.html#numpy.linalg.eigvals)(a) | Compute the eigenvalues of a general matrix.
-[linalg.eigvalsh](https://numpy.org/devdocs/reference/generated/numpy.linalg.eigvalsh.html#numpy.linalg.eigvalsh)(a[, UPLO]) | Compute the eigenvalues of a complex Hermitian or real symmetric matrix.
+[linalg.eig](https://numpy.org/devdocs/reference/generated/numpy.linalg.eig.html#numpy.linalg.eig)(a) | 计算方阵的特征值和右特征向量。
+[linalg.eigh](https://numpy.org/devdocs/reference/generated/numpy.linalg.eigh.html#numpy.linalg.eigh)(a[, UPLO]) | 返回复数Hermitian（共轭对称）或实对称矩阵的特征值和特征向量。
+[linalg.eigvals](https://numpy.org/devdocs/reference/generated/numpy.linalg.eigvals.html#numpy.linalg.eigvals)(a) | 计算通用矩阵的特征值。
+[linalg.eigvalsh](https://numpy.org/devdocs/reference/generated/numpy.linalg.eigvalsh.html#numpy.linalg.eigvalsh)(a[, UPLO]) | 计算复杂的Hermitian或实对称矩阵的特征值。
 
-## Norms and other numbers
+## 范数和其他数字
 
-method | description
+方法 | 描述
 ---|---
-[linalg.norm](https://numpy.org/devdocs/reference/generated/numpy.linalg.norm.html#numpy.linalg.norm)(x[, ord, axis, keepdims]) | Matrix or vector norm.
-[linalg.cond](https://numpy.org/devdocs/reference/generated/numpy.linalg.cond.html#numpy.linalg.cond)(x[, p]) | Compute the condition number of a matrix.
-[linalg.det](https://numpy.org/devdocs/reference/generated/numpy.linalg.det.html#numpy.linalg.det)(a) | Compute the determinant of an array.
-[linalg.matrix_rank](https://numpy.org/devdocs/reference/generated/numpy.linalg.matrix_rank.html#numpy.linalg.matrix_rank)(M[, tol, hermitian]) | Return matrix rank of array using SVD method
-[linalg.slogdet](https://numpy.org/devdocs/reference/generated/numpy.linalg.slogdet.html#numpy.linalg.slogdet)(a) | Compute the sign and (natural) logarithm of the determinant of an array.
-[trace](https://numpy.org/devdocs/reference/generated/numpy.trace.html#numpy.trace)(a[, offset, axis1, axis2, dtype, out]) | Return the sum along diagonals of the array.
+[linalg.norm](https://numpy.org/devdocs/reference/generated/numpy.linalg.norm.html#numpy.linalg.norm)(x[, ord, axis, keepdims]) | 矩阵或向量范数。
+[linalg.cond](https://numpy.org/devdocs/reference/generated/numpy.linalg.cond.html#numpy.linalg.cond)(x[, p]) | 计算矩阵的条件数。
+[linalg.det](https://numpy.org/devdocs/reference/generated/numpy.linalg.det.html#numpy.linalg.det)(a) | 计算数组的行列式。
+[linalg.matrix_rank](https://numpy.org/devdocs/reference/generated/numpy.linalg.matrix_rank.html#numpy.linalg.matrix_rank)(M[, tol, hermitian]) | 使用SVD方法返回数组的矩阵的rank
+[linalg.slogdet](https://numpy.org/devdocs/reference/generated/numpy.linalg.slogdet.html#numpy.linalg.slogdet)(a) | 计算数组行列式的符号和（自然）对数。
+[trace](https://numpy.org/devdocs/reference/generated/numpy.trace.html#numpy.trace)(a[, offset, axis1, axis2, dtype, out]) | 返回数组对角线的和。
 
-## Solving equations and inverting matrices
+## 解方程和逆矩阵
 
-method | description
+方法 | 描述
 ---|---
-[linalg.solve](https://numpy.org/devdocs/reference/generated/numpy.linalg.solve.html#numpy.linalg.solve)(a, b) | Solve a linear matrix equation, or system of linear scalar equations.
-[linalg.tensorsolve](https://numpy.org/devdocs/reference/generated/numpy.linalg.tensorsolve.html#numpy.linalg.tensorsolve)(a, b[, axes]) | Solve the tensor equation a x = b for x.
-[linalg.lstsq](https://numpy.org/devdocs/reference/generated/numpy.linalg.lstsq.html#numpy.linalg.lstsq)(a, b[, rcond]) | Return the least-squares solution to a linear matrix equation.
-[linalg.inv](https://numpy.org/devdocs/reference/generated/numpy.linalg.inv.html#numpy.linalg.inv)(a) | Compute the (multiplicative) inverse of a matrix.
-[linalg.pinv](https://numpy.org/devdocs/reference/generated/numpy.linalg.pinv.html#numpy.linalg.pinv)(a[, rcond, hermitian]) | Compute the (Moore-Penrose) pseudo-inverse of a matrix.
-[linalg.tensorinv](https://numpy.org/devdocs/reference/generated/numpy.linalg.tensorinv.html#numpy.linalg.tensorinv)(a[, ind]) | Compute the ‘inverse’ of an N-dimensional array.
+[linalg.solve](https://numpy.org/devdocs/reference/generated/numpy.linalg.solve.html#numpy.linalg.solve)(a, b) | 求解线性矩阵方程或线性标量方程组。
+[linalg.tensorsolve](https://numpy.org/devdocs/reference/generated/numpy.linalg.tensorsolve.html#numpy.linalg.tensorsolve)(a, b[, axes]) | 对x求解张量方程a x = b。
+[linalg.lstsq](https://numpy.org/devdocs/reference/generated/numpy.linalg.lstsq.html#numpy.linalg.lstsq)(a, b[, rcond]) | 返回线性矩阵方程的最小二乘解。
+[linalg.inv](https://numpy.org/devdocs/reference/generated/numpy.linalg.inv.html#numpy.linalg.inv)(a) | 计算矩阵的（乘法）逆。
+[linalg.pinv](https://numpy.org/devdocs/reference/generated/numpy.linalg.pinv.html#numpy.linalg.pinv)(a[, rcond, hermitian]) | 计算矩阵的（Moore-Penrose）伪逆。
+[linalg.tensorinv](https://numpy.org/devdocs/reference/generated/numpy.linalg.tensorinv.html#numpy.linalg.tensorinv)(a[, ind]) | 计算N维数组的“逆”。
 
-## Exceptions
+## 例外
 
-method | description
+方法 | 描述
 ---|---
-[linalg.LinAlgError](https://numpy.org/devdocs/reference/generated/numpy.linalg.LinAlgError.html#numpy.linalg.LinAlgError) | Generic Python-exception-derived object raised by linalg functions.
-
-## Linear algebra on several matrices at once
-
-*New in version 1.8.0.* 
-
-Several of the linear algebra routines listed above are able to
-compute results for several matrices at once, if they are stacked into
-the same array.
-
-This is indicated in the documentation via input parameter
-specifications such as ``a : (..., M, M) array_like``. This means that
-if for instance given an input array ``a.shape == (N, M, M)``, it is
-interpreted as a “stack” of N matrices, each of size M-by-M. Similar
-specification applies to return values, for instance the determinant
-has ``det : (...)`` and will in this case return an array of shape
-``det(a).shape == (N,)``. This generalizes to linear algebra
-operations on higher-dimensional arrays: the last 1 or 2 dimensions of
-a multidimensional array are interpreted as vectors or matrices, as
-appropriate for each operation.
+[linalg.LinAlgError](https://numpy.org/devdocs/reference/generated/numpy.linalg.LinAlgError.html#numpy.linalg.LinAlgError) | 泛型Python-linalg函数引发的异常派生对象。
+
+## 一次在多个矩阵上的线性代数
+
+*1.8.0版中的新功能* 
+
+上面列出的几个线性代数例程能够一次计算几个矩阵的结果，如果它们堆叠在同一数组中的话。
+
+这在文档中通过输入参数规范（如 ``a : (..., M, M) array_like`` ）表示。
+这意味着，例如，如果给定输入数组 ``a.shape == (N, M, M)`` ，则将其解释为N个矩阵的“堆栈”，
+每个矩阵的大小为M×M。类似的规范也适用于返回值，
+例如行列式 ``det : (...)`` 。并且在这种情况下将返回形状 ``det(a).shape == (N,)`` 的数组。
+这推广到对高维数组的线性代数操作：多维数组的最后1或2维被解释为向量或矩阵，视每个操作而定。