Multiplication: *

If A and B are two scalars, then A * B is the product of A and B.

If one of A and B is a scalar and the other is a matrix, the result is a matrix of the same size, whose entries are the products of the value of the scalar and the entries of the matrix. For example

>>   x = 2;
>>   y = -9;
>>   x * y
      -18
>>   A = [3, 5; 2, -8];
>>   3 * A
       9     15
       6    -24

>>   A * 7
       21    35
       14   -56

If A and B are non-scalar matrices, then A * B is the matrix multiplication of A and B. This is defined only when the sizes of A and B match, i.e., the number of columns of A equals the number of rows of B. For example

>>   A = [3, 5; 2, -8; 1, 9];

       3   5
       2  -8
       1   9

>>   B = [2, 1, 7; -2, 0, 8]
       
       2   1   7
      -2   0   8

>>   A * B
       -4   3   61
       20   2  -50
      -16   1   79

>>   B * A
       15  65
        2  62
Attempt to multiply matrices whose sizes do not match will cause an error.

If A and B are two lists with the same length , then A * B is the dot product (A#1) * (B#1) + (A#2) * (B#2) + ... + (A#n) * (B#n).

If B is a list with length , and A is a list whose length is and whose each element is again a list with the same length , then A * B is the list of length : ((A#1)*B, (A#2)*B, ..., (A#n)*B).

oz 2009-12-22