Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
•Jason Grout (2008-03): almost a complete rewrite, with bits and pieces from the original implementation
sage.matrix.constructor.block_diagonal_matrix(*sub_matrices, **kwds)
This function is available as block_diagonal_matrix(...) and matrix.block_diagonal(...).
Create a block matrix whose diagonal block entries are given by sub_matrices, with zero elsewhere.
See also block_matrix().
EXAMPLES:
sage: A = matrix(ZZ, 2, [1,2,3,4])
sage: block_diagonal_matrix(A, A)
[1 2|0 0]
[3 4|0 0]
[---+---]
[0 0|1 2]
[0 0|3 4]
The sub-matrices need not be square:
sage: B = matrix(QQ, 2, 3, range(6))
sage: block_diagonal_matrix(~A, B)
[ -2 1| 0 0 0]
[ 3/2 -1/2| 0 0 0]
[---------+--------------]
[ 0 0| 0 1 2]
[ 0 0| 3 4 5]
sage.matrix.constructor.block_matrix(*args, **kwds)
This function is available as block_matrix(...) and matrix.block(...).
Returns a larger matrix made by concatenating submatrices (rows first, then columns). For example, the matrix
[ A B ]
[ C D ]
is made up of submatrices A, B, C, and D.
INPUT:
The block_matrix command takes a list of submatrices to add as blocks, optionally preceded by a ring and the
number of block rows and block columns, and returns a matrix.
The submatrices can be specified as a list of matrices (using nrows and ncols to determine their layout), or a
list of lists of matrices, where each list forms a row.
•ring - the base ring
•nrows - the number of block rows
•ncols - the number of block cols
•sub_matrices - matrices (see below for syntax)
•subdivide - boolean, whether or not to add subdivision information to the matrix
•sparse - boolean, whether to make the resulting matrix sparse
EXAMPLES:
sage: A = matrix(QQ, 2, 2, [3,9,6,10])
sage: block_matrix([ [A, -A], [~A, 100*A] ])
[ 3 9| -3 -9]
[ 6 10| -6 -10]
22 Chapter 2. Matrix Constructor