Manuals/calci/MATRIXMULTIPLY

MATRIXMULTIPLY(a,b)

• where $a$ and $b$ are the array of two matrices.

Description

• This function gives product of two matrices.
• Matrix multiplication is of two types:

Type 1: A scalar (a constant) is multiplied with the each element of the matrix.
Type 2: Multiplication of two matrices. 

• We can do the matrix multiplication when the number of columns in the first matrix equals the number of rows in the second matrix.
• For e.g. 4x2 matrix can multiply with 2x3. The matrix product of two arrays $a$ and $b$ is: $x_{ij}=\sum _{k=1}^{n}a_{ik}.b_{kj}$ where $i$ is the row number and $j$ is the column number.
• i.e Multiply the elements of each row of 1st matrix by elements of each column of 2nd matrix.
• So the resultant mat

rix is of the order: Rows of 1st matrix × Columns of 2nd.

• For e.g If we multiply a 4x2 matrix with a 2x3 matrix, the product matrix is of order 4x3.
• Matrix multiplication satisfies the associative and distributive properties.But it is not satisfies the commutative property.
• i.e., Let A,B and C are three matrices, then A(BC)= (AB)C (Associative property)
• A(B+C)= AB+AC and (A+B)C = AC+BC (Distributive properties)
• k(AB)=(kA)B=A(kB)where k is a constant.But $AB\neq BA$ (Commutative property)

Examples

1. MATRIXMULTIPLY([2,-3,4;-5,6,7],9)

18	-27	36
-45	54	63

2. MATRIXMULTIPLY([4,7.2,6;9,-8,12],[2,3;6,5;9,8])

105.2	96
78	83

See Also

• MINVERSE
• MMULT
• MDETERM

References

Matrix Multiplication

• List of Main Z Functions

• Z3 home