Elements of matrix spaces are of class Matrix
. They can be
either sparse or dense, and can be defined over any base ring.
We create the
matrix
as an element of a matrix space over
:
sage: M = MatrixSpace(RationalField(),2,3)
sage: A = M([1,2,3, 4,5,6])
sage: A
[1 2 3]
[4 5 6]
sage: A.parent()
Full MatrixSpace of 2 by 3 dense matrices over Rational Field
We next change the top-right entry of
. Note that matrix indexing
is 0
-based in SAGE, so the top right entry is
, which should
be thought of as ``row number 0
, column number 2''.
sage: A[0,2] = 389
sage: A
[ 1 2 389]
[ 4 5 6]
Also notice how matrices print. All columns have the same width and
entries in a given column are right justified. Next we compute the
reduced row echelon form of
.
sage: A.echelon_form()
[ 1 0 -1933/3]
[ 0 1 1550/3]
The module matrix.matrix defines the following methods:
_sparse_dot_product( |
v, w) |
-
v and w are dictionaries with integer keys.
-
Find minimal polynomial of a linear recurrence sequence.
The module matrix.matrix defines the following classes:
- class Matrix
-
The Matrix class is the base class for all matrix
classes.
- class Matrix_dense_integer
- class Matrix_dense_rational
-
The Matrix_dense_rational class derives from
Matrix, and defines functionality for dense matrices over
the field
of rational numbers.
- class Matrix_domain
- class Matrix_field
- class Matrix_generic_dense
-
The Matrix_generic_dense class derives from
Matrix, and defines functionality for dense matrices over
any base ring.
- class Matrix_generic_dense_domain
- class Matrix_generic_dense_field
- class Matrix_generic_dense_pid
- class Matrix_generic_sparse
-
The Matrix_generic_sparse class derives from
Matrix, and defines functionality for dense matrices over
any base ring.
- class Matrix_generic_sparse_domain
- class Matrix_generic_sparse_field
- class Matrix_generic_sparse_pid
- class Matrix_integer
- class Matrix_pid
- class Matrix_sparse_integer
- class Matrix_sparse_rational
-
The Matrix_sparse_rational class derives from
Matrix, and defines functionality for sparse matrices
over the field
of rational numbers.
Release 0.7.7, documentation updated on October 4, 2005.
See About this document... for information on suggesting changes.