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Signed-off-by: David Rotermund <54365609+davrot@users.noreply.github.com>
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# Linear algebra
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{:.no_toc}
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<nav markdown="1" class="toc-class">
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* TOC
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{:toc}
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</nav>
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## The goal
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Questions to [David Rotermund](mailto:davrot@uni-bremen.de)
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The @ operator
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Introduced in NumPy 1.10.0, the @ operator is preferable to other methods when computing the matrix product between 2d arrays. The numpy.matmul function implements the @ operator.
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## [numpy.linalg](https://numpy.org/doc/stable/reference/routines.linalg.html)
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### Matrix and vector products
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|[dot(a, b[, out])](https://numpy.org/doc/stable/reference/generated/numpy.dot.html#numpy.dot)|Dot product of two arrays.|
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|[linalg.multi_dot(arrays, *[, out])](https://numpy.org/doc/stable/reference/generated/numpy.linalg.multi_dot.html#numpy.linalg.multi_dot)|Compute the dot product of two or more arrays in a single function call, while automatically selecting the fastest evaluation order.|
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|[vdot(a, b, /)](https://numpy.org/doc/stable/reference/generated/numpy.vdot.html#numpy.vdot)|Return the dot product of two vectors.|
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|[inner(a, b, /)](https://numpy.org/doc/stable/reference/generated/numpy.inner.html#numpy.inner)|Inner product of two arrays.|
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|[outer(a, b[, out])](https://numpy.org/doc/stable/reference/generated/numpy.outer.html#numpy.outer)|Compute the outer product of two vectors.|
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|[matmul(x1, x2, /[, out, casting, order, ...])](https://numpy.org/doc/stable/reference/generated/numpy.matmul.html#numpy.matmul)|Matrix product of two arrays.|
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|[tensordot(a, b[, axes])](https://numpy.org/doc/stable/reference/generated/numpy.tensordot.html#numpy.tensordot)|Compute tensor dot product along specified axes.|
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|[einsum(subscripts, *operands[, out, dtype, ...])](https://numpy.org/doc/stable/reference/generated/numpy.einsum.html#numpy.einsum)|Evaluates the Einstein summation convention on the operands.|
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|[einsum_path(subscripts, *operands[, optimize])](https://numpy.org/doc/stable/reference/generated/numpy.einsum_path.html#numpy.einsum_path)|Evaluates the lowest cost contraction order for an einsum expression by considering the creation of intermediate arrays.|
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|[linalg.matrix_power(a, n)](https://numpy.org/doc/stable/reference/generated/numpy.linalg.matrix_power.html#numpy.linalg.matrix_power)|Raise a square matrix to the (integer) power n.|
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|[kron(a, b)](https://numpy.org/doc/stable/reference/generated/numpy.kron.html#numpy.kron)|Kronecker product of two arrays.|
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### Decompositions
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|[linalg.cholesky(a)](https://numpy.org/doc/stable/reference/generated/numpy.linalg.cholesky.html#numpy.linalg.cholesky)|Cholesky decomposition.|
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|[linalg.qr(a[, mode])](https://numpy.org/doc/stable/reference/generated/numpy.linalg.qr.html#numpy.linalg.qr)|Compute the qr factorization of a matrix.|
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|[linalg.svd(a[, full_matrices, compute_uv, ...])](https://numpy.org/doc/stable/reference/generated/numpy.linalg.svd.html#numpy.linalg.svd)|Singular Value Decomposition.|
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### Matrix eigenvalues
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|[linalg.eig(a)](https://numpy.org/doc/stable/reference/generated/numpy.linalg.eig.html#numpy.linalg.eig)|Compute the eigenvalues and right eigenvectors of a square array.|
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|[linalg.eigh(a[, UPLO])](https://numpy.org/doc/stable/reference/generated/numpy.linalg.eigh.html#numpy.linalg.eigh)|Return the eigenvalues and eigenvectors of a complex Hermitian (conjugate symmetric) or a real symmetric matrix.|
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|[linalg.eigvals(a)](https://numpy.org/doc/stable/reference/generated/numpy.linalg.eigvals.html#numpy.linalg.eigvals)|Compute the eigenvalues of a general matrix.|
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|[linalg.eigvalsh(a[, UPLO])](https://numpy.org/doc/stable/reference/generated/numpy.linalg.eigvalsh.html#numpy.linalg.eigvalsh)|Compute the eigenvalues of a complex Hermitian or real symmetric matrix.|
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### Norms and other numbers
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|[linalg.norm(x[, ord, axis, keepdims])](https://numpy.org/doc/stable/reference/generated/numpy.linalg.norm.html#numpy.linalg.norm)|Matrix or vector norm.|
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|[linalg.cond(x[, p])](https://numpy.org/doc/stable/reference/generated/numpy.linalg.cond.html#numpy.linalg.cond)|Compute the condition number of a matrix.|
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|[linalg.det(a)](https://numpy.org/doc/stable/reference/generated/numpy.linalg.det.html#numpy.linalg.det)|Compute the determinant of an array.|
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|[linalg.matrix_rank(A[, tol, hermitian])](https://numpy.org/doc/stable/reference/generated/numpy.linalg.matrix_rank.html#numpy.linalg.matrix_rank)|Return matrix rank of array using SVD method|
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|[linalg.slogdet(a)](https://numpy.org/doc/stable/reference/generated/numpy.linalg.slogdet.html#numpy.linalg.slogdet)|Compute the sign and (natural) logarithm of the determinant of an array.|
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|[trace(a[, offset, axis1, axis2, dtype, out])](https://numpy.org/doc/stable/reference/generated/numpy.trace.html#numpy.trace)|Return the sum along diagonals of the array.|
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### Solving equations and inverting matrices
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|[linalg.solve(a, b)](https://numpy.org/doc/stable/reference/generated/numpy.linalg.solve.html#numpy.linalg.solve)|Solve a linear matrix equation, or system of linear scalar equations.|
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|[linalg.tensorsolve(a, b[, axes])](https://numpy.org/doc/stable/reference/generated/numpy.linalg.tensorsolve.html#numpy.linalg.tensorsolve)|Solve the tensor equation a x = b for x.|
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|[linalg.lstsq(a, b[, rcond])](https://numpy.org/doc/stable/reference/generated/numpy.linalg.lstsq.html#numpy.linalg.lstsq)|Return the least-squares solution to a linear matrix equation.|
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|[linalg.inv(a)](https://numpy.org/doc/stable/reference/generated/numpy.linalg.inv.html#numpy.linalg.inv)|Compute the (multiplicative) inverse of a matrix.|
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|[linalg.pinv(a[, rcond, hermitian])](https://numpy.org/doc/stable/reference/generated/numpy.linalg.pinv.html#numpy.linalg.pinv)|Compute the (Moore-Penrose) pseudo-inverse of a matrix.|
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|[linalg.tensorinv(a[, ind])](https://numpy.org/doc/stable/reference/generated/numpy.linalg.tensorinv.html#numpy.linalg.tensorinv)|Compute the 'inverse' of an N-dimensional array.|
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