Sage Reference Manual: Matrices and Spaces of Matrices

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.2[-----------+-----------][-5/12 3/8| 300 900][ 1/4 -1/8| 600 1000]If the number of submatrices in each row is the same, you can specify the submatrices as a single list too:sage: block_matrix(2, 2, [ A, A, A, A ])[ 3 9| 3 9][ 6 10| 6 10][-----+-----][ 3 9| 3 9][ 6 10| 6 10]One can use constant entries:sage: block_matrix([ [1, A], [0, 1] ])[ 1 0| 3 9][ 0 1| 6 10][-----+-----][ 0 0| 1 0][ 0 0| 0 1]A zero entry may represent any square or non-square zero matrix:sage: B = matrix(QQ, 1, 1, [ 1 ] )sage: C = matrix(QQ, 2, 2, [ 2, 3, 4, 5 ] )sage: block_matrix([ [B, 0], [0, C] ])[1|0 0][-+---][0|2 3][0|4 5]One can specify the number of rows or columns as keywords too:sage: block_matrix([A, -A, ~A, 100*A], ncols=4)[ 3 9| -3 -9|-5/12 3/8| 300 900][ 6 10| -6 -10| 1/4 -1/8| 600 1000]sage: block_matrix([A, -A, ~A, 100*A], nrows=1)[ 3 9| -3 -9|-5/12 3/8| 300 900][ 6 10| -6 -10| 1/4 -1/8| 600 1000]It handles base rings nicely too:sage: R. = ZZ[’x’]sage: block_matrix(2, 2, [1/2, A, 0, x-1])[ 1/2 0| 3 9][ 0 1/2| 6 10][-----------+-----------][ 0 0|x - 1 0][ 0 0| 0 x - 1]sage: block_matrix(2, 2, [1/2, A, 0, x-1]).parent()Full MatrixSpace of 4 by 4 dense matrices over Univariate Polynomial Ring in x over Rational FieSubdivisions are optional. If they are disabled, the columns need not line up:sage: B = matrix(QQ, 2, 3, range(6))sage: block_matrix([ [~A, B], [B, ~A] ], subdivide=False)[-5/12 3/8 0 1 2]23