Scilab fundamentals 5 - Elementary matrix operations

²  Matrix arithmetic: addition, subtraction, multiplication, and backslash

    The common operators including +, -, and*, applied on real numbers are also available with real matrices. The operator, named backslash or left division, calculate the solution of A^-1B which represented as A\B. These matrix arithmetic operators are performed on matrix to matrix operation, and the operation rules are defined by linear algebra. Therefore, the dimensions of matrices must be the same for additions of matrices, i.e., two m×n matrices or two square matrices. For multiplication, A is a m-by-n matrix and B is a n-by-m matrix. As for backslash, A is a m-by-m matrix, and B is a m-by-n matrix.

²  Elementwise operations

    

    To perform multiplication and backslash element to element, a dot is added before the operators, *, and \. Because these two elementwise operators, .* and .\, perform operations on elements directly, the dimensions of A and B are both m-by-n.