Sage Reference Manual: Matrices and Spaces of Matrices

CHAPTERTWOMATRIX CONSTRUCTORclass sage.matrix.constructor.MatrixFactoryBases: objectCreate a matrix.This implements the matrix constructor:sage: matrix([[1,2],[3,4]])[1 2][3 4]It also contains methods to create special types of matrices, see matrix.[tab] for more options. For example:sage: matrix.identity(2)[1 0][0 1]INPUT:The matrix command takes the entries of a matrix, optionally preceded by a ring and the dimensions of thematrix, and returns a matrix.The entries of a matrix can be specified as a flat list of elements, a list of lists (i.e., a list of rows), a list ofSage vectors, a callable object, or a dictionary having positions as keys and matrix entries as values (see theexamples). If you pass in a callable object, then you must specify the number of rows and columns. You cancreate a matrix of zeros by passing an empty list or the integer zero for the entries. To construct a multiple of theidentity (cI), you can specify square dimensions and pass in c. Calling matrix() with a Sage object may returnsomething that makes sense. Calling matrix() with a NumPy array will convert the array to a matrix.The ring, number of rows, and number of columns of the matrix can be specified by setting the ring, nrows, orncols parameters or by passing them as the first arguments to the function in the order ring, nrows, ncols. Thering defaults to ZZ if it is not specified or cannot be determined from the entries. If the numbers of rows andcolumns are not specified and cannot be determined, then an empty 0x0 matrix is returned.•ring - the base ring for the entries of the matrix.•nrows - the number of rows in the matrix.•ncols - the number of columns in the matrix.•sparse - create a sparse matrix. This defaults to True when the entries are given as a dictionary, otherwisedefaults to False.OUTPUT:a matrix15