Linear algebra

Matrix and vector products

dpnp.dot	Dot product of a and b.
dpnp.linalg.multi_dot	Compute the dot product of two or more arrays in a single function call.
dpnp.vdot	Return the dot product of two vectors.
dpnp.vecdot	Computes the vector dot product.
dpnp.linalg.vecdot	Computes the vector dot product.
dpnp.inner	Returns the inner product of two arrays.
dpnp.outer	Returns the outer product of two arrays.
dpnp.matmul	Matrix product of two arrays.
dpnp.linalg.matmul	Computes the matrix product.
dpnp.matvec	Matrix-vector dot product of two arrays.
dpnp.vecmat	Vector-matrix dot product of two arrays.
dpnp.tensordot	Compute tensor dot product along specified axes.
dpnp.linalg.tensordot	Compute tensor dot product along specified axes.
dpnp.einsum	einsum(subscripts, *operands, out=None, dtype=None, order="K", casting="same_kind", optimize=False)
dpnp.einsum_path	einsum_path(subscripts, *operands, optimize="greedy")
dpnp.linalg.matrix_power	Raise a square matrix to the (integer) power n.
dpnp.kron	Kronecker product of two arrays.
dpnp.linalg.cross	Returns the cross product of 3-element vectors.

Decompositions

dpnp.linalg.cholesky	Cholesky decomposition.
dpnp.linalg.outer	Compute the outer product of two vectors.
dpnp.linalg.qr	Compute the qr factorization of a matrix.
dpnp.linalg.svd	Singular Value Decomposition.
dpnp.linalg.svdvals	Returns the singular values of a matrix (or a stack of matrices) x.

Matrix eigenvalues

dpnp.linalg.eig	Compute the eigenvalues and right eigenvectors of a square array.
dpnp.linalg.eigh	Return the eigenvalues and eigenvectors of a complex Hermitian (conjugate symmetric) or a real symmetric matrix.
dpnp.linalg.eigvals	Compute the eigenvalues of a general matrix.
dpnp.linalg.eigvalsh	Compute the eigenvalues of a complex Hermitian or real symmetric matrix.

Norms and other numbers

dpnp.linalg.norm	Matrix or vector norm.
dpnp.linalg.matrix_norm	Computes the matrix norm of a matrix (or a stack of matrices) x.
dpnp.linalg.vector_norm	Computes the vector norm of a vector (or batch of vectors) x.
dpnp.linalg.cond	Compute the condition number of a matrix.
dpnp.linalg.det	Compute the determinant of an array.
dpnp.linalg.matrix_rank	Return matrix rank of array using SVD method.
dpnp.linalg.slogdet	Compute the sign and (natural) logarithm of the determinant of an array.
dpnp.trace	Return the sum along diagonals of the array.
dpnp.linalg.trace	Returns the sum along the specified diagonals of a matrix (or a stack of matrices) x.

Solving linear equations

dpnp.linalg.solve	Solve a linear matrix equation, or system of linear scalar equations.
dpnp.linalg.tensorsolve	Solve the tensor equation a x = b for x.
dpnp.linalg.lstsq	Return the least-squares solution to a linear matrix equation.
dpnp.linalg.inv	Compute the (multiplicative) inverse of a matrix.
dpnp.linalg.pinv	Compute the (Moore-Penrose) pseudo-inverse of a matrix.
dpnp.linalg.tensorinv	Compute the 'inverse' of an N-dimensional array.

Other matrix operations

dpnp.diagonal	Return specified diagonals.
dpnp.linalg.diagonal	Returns specified diagonals of a matrix (or a stack of matrices) x.
dpnp.linalg.matrix_transpose	Transposes a matrix (or a stack of matrices) x.

Exceptions

dpnp.linalg.LinAlgError

Generic Python-exception-derived object raised by LinAlg functions.

Linear algebra on several matrices at once

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) {dpnp.ndarray, usm_ndarray}. 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.