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 sage.linalg.matrix defines the following classes:
- class Matrix
-
The Matrix class is the base class for all matrix
classes. To create a Matrix, first create a
MatrixSpace, then coerce a list of elements into the
MatrixSpace. See the documentation of
MatrixSpace for more details.
- class Matrix_generic_dense
-
The Matrix_generic_dense class derives from
Matrix, and defines functionality for dense matrices over
any base ring. Matrices are represented by a list of elements in
the base ring, and element access operations are implemented in
this class.
- class Matrix_generic_sparse
-
The Matrix_generic_sparse class derives from
Matrix, and defines functionality for dense matrices over
any base ring. A generic sparse matrix is represented using a
dictionary with keys pairs
and values in the base ring.
- class Matrix_rational_dense
-
The Matrix_rational_dense class derives from
Matrix, and defines functionality for dense matrices over
the field
of rational numbers.
- class Matrix_rational_sparse
-
The Matrix_rational_sparse class derives from
Matrix, and defines functionality for sparse matrices
over the field
of rational numbers.
The module sage.linalg.matrix defines the following methods:
-
Find minimal polynomial of a linear recurrence sequence.
Release 0.5.alpha7, documentation updated on August 5, 2005.
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