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]
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