# probnum.linops¶

Finite-dimensional Linear Operators.

This package implements finite dimensional linear operators. It can be used to represent linear maps between finite-dimensional vector spaces without explicitly constructing their matrix representation in memory. This is particularly useful for sparse and structured matrices and often allows for the definition of a more efficient matrix-vector product. Linear operators support common algebraic operations, including matrix-vector products, addition, multiplication, and transposition.

Several algorithms in the probnum.linalg subpackage are able to operate on LinearOperator instances.

## Functions¶

 Return A as a LinearOperator.

## Classes¶

 LinearOperator(*args, **kwargs) Composite base class for finite-dimensional linear operators. Identity(*args, **kwargs) The identity operator. ScalarMult(*args, **kwargs) A linear operator representing scalar multiplication. MatrixMult(*args, **kwargs) A linear operator defined via a matrix. Kronecker(*args, **kwargs) Kronecker product of two linear operators. SymmetricKronecker(*args, **kwargs) Symmetric Kronecker product of two linear operators. Symmetrize(*args, **kwargs) Symmetrizes a vector in its matrix representation. Vec(*args, **kwargs) Vectorization operator. Svec(*args, **kwargs) Symmetric vectorization operator.