Manuals/calci/MATRIXMULTIPLY
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MATRIXMULTIPLY(a,b)
- where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} is: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_{ij}= \sum_{k=1}^n a_{ik}.b_{kj}} where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i} is the row number and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle AB \ne 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 |
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References