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Examples ======== >>> from sympy.tensor.array.expressions.conv_indexed_to_array import convert_indexed_to_array >>> from sympy.tensor.array import tensorcontraction, tensorproduct >>> from sympy import MatrixSymbol, Sum >>> from sympy.abc import i, j, k, l, N >>> from sympy.tensor.array.expressions.conv_matrix_to_array import convert_matrix_to_array >>> from sympy.tensor.array.expressions.conv_array_to_matrix import convert_array_to_matrix >>> A = MatrixSymbol("A", N, N) >>> B = MatrixSymbol("B", N, N) >>> C = MatrixSymbol("C", N, N) >>> D = MatrixSymbol("D", N, N) >>> expr = Sum(A[i, j]*B[j, k], (j, 0, N-1)) >>> cg = convert_indexed_to_array(expr) >>> convert_array_to_matrix(cg) A*B >>> cg = convert_indexed_to_array(expr, first_indices=[k]) >>> convert_array_to_matrix(cg) B.T*A.T Transposition is detected: >>> expr = Sum(A[j, i]*B[j, k], (j, 0, N-1)) >>> cg = convert_indexed_to_array(expr) >>> convert_array_to_matrix(cg) A.T*B >>> cg = convert_indexed_to_array(expr, first_indices=[k]) >>> convert_array_to_matrix(cg) B.T*A Detect the trace: >>> expr = Sum(A[i, i], (i, 0, N-1)) >>> cg = convert_indexed_to_array(expr) >>> convert_array_to_matrix(cg) Trace(A) Recognize some more complex traces: >>> expr = Sum(A[i, j]*B[j, i], (i, 0, N-1), (j, 0, N-1)) >>> cg = convert_indexed_to_array(expr) >>> convert_array_to_matrix(cg) Trace(A*B) More complicated expressions: >>> expr = Sum(A[i, j]*B[k, j]*A[l, k], (j, 0, N-1), (k, 0, N-1)) >>> cg = convert_indexed_to_array(expr) >>> convert_array_to_matrix(cg) A*B.T*A.T Expressions constructed from matrix expressions do not contain literal indices, the positions of free indices are returned instead: >>> expr = A*B >>> cg = convert_matrix_to_array(expr) >>> convert_array_to_matrix(cg) A*B If more than one line of matrix multiplications is detected, return separate matrix multiplication factors embedded in a tensor product object: >>> cg = tensorcontraction(tensorproduct(A, B, C, D), (1, 2), (5, 6)) >>> convert_array_to_matrix(cg) 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