Sage Reference Manual: Matrices and Spaces of Matrices

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.2sage: ones_matrix(CC)Traceback (most recent call last):...ValueError: constructing an all ones matrix requires at least one dimensionsage.matrix.constructor.prepare(w)Given a list w of numbers, find a common ring that they all canonically map to, and return the list of images ofthe elements of w in that ring along with the ring.This is for internal use by the matrix function.INPUT:•w - listOUTPUT:list, ringEXAMPLES:sage: sage.matrix.constructor.prepare([-2, Mod(1,7)])([5, 1], Ring of integers modulo 7)Notice that the elements must all canonically coerce to a common ring (since Sequence is called):sage: sage.matrix.constructor.prepare([2/1, Mod(1,7)])Traceback (most recent call last):...TypeError: unable to find a common ring for all elementssage.matrix.constructor.prepare_dict(w)Given a dictionary w of numbers, find a common ring that they all canonically map to, and return the dictionaryof images of the elements of w in that ring along with the ring.This is for internal use by the matrix function.INPUT:•w - dictOUTPUT:dict, ringEXAMPLES:sage: sage.matrix.constructor.prepare_dict({(0,1):2, (4,10):Mod(1,7)})({(0, 1): 2, (4, 10): 1}, Ring of integers modulo 7)sage.matrix.constructor.random_diagonalizable_matrix(parent, eigenvalues=None, dimensions=None)This function is available as random_diagonalizable_matrix(...) and matrix.random_diagonalizable(...).Create a random matrix that diagonalizes nicely.To be used as a teaching tool. Return matrices have only real eigenvalues.INPUT:If eigenvalues and dimensions are not specified in a list, they will be assigned randomly.•parent - the desired size of the square matrix.•eigenvalues - the list of desired eigenvalues (default=None).41