Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

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Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1 [-2.0 1.0] [ 1.5 -0.5] To compute eigenvalues the use the functions left_eigenvectors or right_eigenvectors sage: p,e = m.right_eigenvectors() the result of eigen is a pair (p,e), where p is a list of eigenvalues and the e is a matrix whose columns are the eigenvectors. To solve a linear system Ax = b where A = [[1,2],[3,4]] and b = [5,6]. sage: b = vector(RDF,[5,6]) sage: m.solve_right(b) (-4.0, 4.5) See the commands qr, lu, and svd for QR, LU, and singular value decomposition. 396 Chapter 20. Dense matrices over the Real Double Field using NumPy
CHAPTER TWENTYONE DENSE MATRICES OVER THE COMPLEX DOUBLE FIELD USING NUMPY Dense matrices over the Complex Double Field using NumPy EXAMPLES: sage: b=Mat(CDF,2,3).basis() sage: b[0] [1.0 0.0 0.0] [0.0 0.0 0.0] We deal with the case of zero rows or zero columns: sage: m = MatrixSpace(CDF,0,3) sage: m.zero_matrix() [] TESTS: sage: a = matrix(CDF,2,[i+(4-i)*I for i in range(4)], sparse=False) sage: TestSuite(a).run() sage: Mat(CDF,0,0).zero_matrix().inverse() [] AUTHORS: • Jason Grout (2008-09): switch to NumPy backend • Josh Kantor • William Stein: many bug fixes and touch ups. class sage.matrix.matrix_complex_double_dense.Matrix_complex_double_dense Bases: sage.matrix.matrix_double_dense.Matrix_double_dense Class that implements matrices over the real double field. These are supposed to be fast matrix operations using C doubles. Most operations are implemented using numpy which will call the underlying BLAS on the system. EXAMPLES: sage: m = Matrix(CDF, [[1,2*I],[3+I,4]]) sage: m**2 [-1.0 + 6.0*I 10.0*I] [15.0 + 5.0*I 14.0 + 6.0*I] 397
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