Sage Reference Manual: Matrices and Spaces of Matrices

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.2sage: A = matrix(2, 3, range(6))sage: B = matrix(3, 3, range(9))sage: block_matrix([A, A, A, B, B, B])Traceback (most recent call last):...ValueError: must specify nrows or ncols for non-square block matrix.sage.matrix.constructor.column_matrix(*args, **kwds)This function is available as column_matrix(...) and matrix.column(...).Constructs a matrix, and then swaps rows for columns and columns for rows.Note: Linear algebra in Sage favors rows over columns. So, generally, when creating a matrix, input vectorsand lists are treated as rows. This function is a convenience that turns around this convention when creating amatrix. If you are not familiar with the usual matrix constructor, you might want to consider it first.INPUT:Inputs are almost exactly the same as for the matrix constructor, which are documented there. But see examplesbelow for how dimensions are handled.OUTPUT:Output is exactly the transpose of what the matrix constructor would return. In other words, the matrixconstructor builds a matrix and then this function exchanges rows for columns, and columns for rows.EXAMPLES:The most compelling use of this function is when you have a collection of lists or vectors that you would liketo become the columns of a matrix. In almost any other situation, the matrix constructor can probably do thejob just as easily, or easier.sage: col_1 = [1,2,3]sage: col_2 = [4,5,6]sage: column_matrix([col_1, col_2])[1 4][2 5][3 6]sage: v1 = vector(QQ, [10, 20])sage: v2 = vector(QQ, [30, 40])sage: column_matrix(QQ, [v1, v2])[10 30][20 40]If you only specify one dimension along with a flat list of entries, then it will be the number of columns in theresult (which is different from the behavior of the matrix constructor).sage: column_matrix(ZZ, 8, range(24))[ 0 3 6 9 12 15 18 21][ 1 4 7 10 13 16 19 22][ 2 5 8 11 14 17 20 23]And when you specify two dimensions, then they should be number of columns first, then the number of rows,which is the reverse of how they would be specified for the matrix constructor.sage: column_matrix(QQ, 5, 3, range(15))[ 0 3 6 9 12][ 1 4 7 10 13][ 2 5 8 11 14]25