Linear algebra

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Need to implement following functions as described here Linear algebra

Matrix and vector products

• dot(a, b[, out]) Dot product of two arrays.
• linalg.multi_dot(arrays, *[, out]) 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(x1, x2, /[, out, casting, order, …]) Matrix product of two arrays.
• tensordot(a, b[, axes]) Compute tensor dot product along specified axes.
• 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(a, 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 complex Hermitian (conjugate symmetric) or a real symmetric matrix.
• linalg.eigvals(a) Compute the eigenvalues of a general matrix.
• linalg.eigvalsh(a[, UPLO]) Compute the eigenvalues of a complex Hermitian or real symmetric matrix.

Norms and other numbers

• linalg.norm(x[, ord, axis, keepdims]) Matrix or vector norm.
• 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

• 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, hermitian]) 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.