Binary operators

The package supports binary operations

    X = A + B      // matrix addition
    X = A - B      // matrix subtraction
    X = A * B      // matrix multiplication
    X = A.i() * B  // equation solve (square matrix A)
    X = A | B      // concatenate horizontally (concatenate the rows)
    X = A & B      // concatenate vertically (concatenate the columns)
    X = SP(A, B)   // elementwise product of A and B (Schur product)

Notes:

• If you are doing repeated multiplication. For example A*B*C, use brackets to force the order of evaluation to minimize the number of operations. If C is a column vector and A is not a vector, then it will usually reduce the number of operations to use A*(B*C).
• In the equation solve example case the inverse is not explicitly calculated. An LU decomposition of A is performed and this is applied to B. This is more efficient than calculating the inverse and then multiplying. See also multiple matrix solving.
• The package does not (yet?) recognise B*A.i() as an equation solve and the inverse of A would be calculated. It is probably better to use (A.t().i()*B.t()).t().
• Horizontal or vertical concatenation returns a result of type Matrix, RowVector or ColumnVector.
• If A is m x p, B is m x q, then A | B is m x (p+q) with the k-th row being the elements of the k-th row of A followed by the elements of the k-th row of B.
• If A is p x n, B is q x n, then A & B is (p+q) x n with the k-th column being the elements of the k-th column of A followed by the elements of the k-th column of B.
• For complicated concatenations of matrices, consider instead using submatrices.