.. _ch:matrices: Matrices and Spaces of Matrices =============================== Sage provides native support for working with matrices over any commutative or noncommutative ring. The parent object for a matrix is a matrix space ``MatrixSpace(R, n, m)`` of all :math:`n\times m` matrices over a ring :math:`R`. To create a matrix, either use the ``matrix(...)`` function or create a matrix space using the ``MatrixSpace`` command and coerce an object into it. Matrices also act on row vectors, which you create using the ``vector(...)`` command or by making a ``VectorSpace`` and coercing lists into it. The natural action of matrices on row vectors is from the right. Sage currently does not have a column vector class (on which matrices would act from the left), but this is planned. In addition to native Sage matrices, Sage also includes the following additional ways to compute with matrices: - Several math software systems included with Sage have their own native matrix support, which can be used from Sage. E.g., PARI, GAP, Maxima, and Singular all have a notion of matrices. - The GSL C-library is included with Sage, and can be used via Cython. - The ``scipy`` module provides support for *sparse* numerical linear algebra, among many other things. - The ``numpy`` module, which you load by typing ``import numpy`` is included standard with Sage. It contains a very sophisticated and well developed array class, plus optimized support for *numerical linear algebra*. Sage's matrices over RDF and CDF (native floating-point real and complex numbers) use numpy. Finally, this module contains some data-structures for matrix-like objects like operation tables (e.g. the multiplication table of a group). .. toctree:: :maxdepth: 2 sage/matrix/matrix_space sage/matrix/constructor sage/matrix/docs sage/matrix/matrix sage/matrix/matrix0 sage/matrix/matrix1 sage/matrix/matrix2 sage/matrix/strassen sage/matrix/berlekamp_massey sage/matrix/matrix_dense sage/matrix/matrix_sparse sage/matrix/matrix_generic_dense sage/matrix/matrix_generic_sparse sage/matrix/matrix_modn_dense sage/matrix/matrix_modn_sparse sage/matrix/matrix_symbolic_dense sage/matrix/matrix_integer_dense sage/matrix/matrix_rational_dense sage/matrix/matrix_double_dense sage/matrix/matrix_real_double_dense sage/matrix/matrix_complex_double_dense sage/matrix/operation_table sage/matrix/benchmark
