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 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
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.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