Language Reference |
Multiplication Operator, Elementwise: # |
The elementwise multiplication operator (#) computes a new matrix with elements that are the products of the corresponding elements of matrix1 and matrix2.
For example, the following statements compute the matrix ab, shown in Figure 23.17:
a = {1 2, 3 4}; b = {4 8, 0 5}; ab = a#b; print ab;
In addition to multiplying matrices that have the same dimensions, you can use the elementwise multiplication operator to multiply a matrix and a scalar.
When either argument is a scalar, each element in matrix is multiplied by the scalar value.
When you use the matrix # vector form, each row or column of the matrix is multiplied by a corresponding element of the vector.
If you multiply by an column vector, each row of the matrix is multiplied by the corresponding row of the vector.
If you multiply by a row vector, each column of the matrix is multiplied by the corresponding column of the vector.
For example, a matrix can be multiplied on either side by a , , , or matrix. The following statements multiply the matrix a by a column vector and a row vector. The results are shown in Figure 23.18.
c = {10, 100}; /* column vector */ r = {10 100}; /* row vector */ ac = a#c; ar = a#r; print ac, ar;
Elementwise multiplication is also known as the Schur or Hadamard product. Elementwise multiplication (which uses the # operator) should not be confused with matrix multiplication (which uses the * operator).
When an element of a matrix contains a missing value, the corresponding element of the product is also a missing value.
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