# probnum.linalg¶

## probnum.linalg¶

Linear Algebra.

This package implements common operations and (probabilistic) numerical methods for linear algebra.

### Functions¶

 problinsolve(A, b[, A0, Ainv0, x0, …]) Infer a solution to the linear system $$A x = b$$ in a Bayesian framework. bayescg(A, b[, x0, maxiter, atol, rtol, …]) Conjugate Gradients using prior information on the solution of the linear system.

### Classes¶

 ProbabilisticLinearSolver(A, b) An abstract base class for probabilistic linear solvers. MatrixBasedSolver(A, b[, x0]) Abstract class for matrix-based probabilistic linear solvers. AsymmetricMatrixBasedSolver(A, b, x0) Asymmetric matrix-based probabilistic linear solver. SymmetricMatrixBasedSolver(A, b[, A0, Ainv0, x0]) Symmetric matrix-based probabilistic linear solver. SolutionBasedSolver(A, b[, x0]) Solver iteration of BayesCG.

## probnum.linalg.linops¶

(Finite-dimensional) Linear Operators.

This package implements a variety of finite dimensional linear operators. These have the advantage of only implementing a matrix-vector product instead of representing the full linear operator as a matrix in memory.

### Functions¶

 aslinop(A) Return A as a LinearOperator.

### Classes¶

 LinearOperator(dtype, shape) Finite dimensional linear operators. Identity(shape) The identity operator. ScalarMult(shape, scalar) A linear operator representing scalar multiplication. MatrixMult(A) A linear operator defined via a matrix. Kronecker(A, B[, dtype]) Kronecker product of two linear operators. SymmetricKronecker(A[, B, dtype]) Symmetric Kronecker product of two linear operators. Vec([order, dim]) Vectorization operator. Svec(dim[, check_symmetric]) Symmetric vectorization operator. Symmetrize(dim) Symmetrizes a vector in its matrix representation.