Devika: /* Examples */

2019-04-17T18:55:04Z

Examples

Devika: Created page with "
'''MATRIXPRODUCT (a,b,ConsiderUnits)'''

where $a$ and $b$ are the array of two matrices ==Description== This fu..."

2017-06-21T22:41:53Z

Created page with "<div style="font-size:30px">'''MATRIXPRODUCT (a,b,ConsiderUnits)'''</div><br/> *where <math>a</math> and <math>b</math> are the array of two matrices ==Description== *This fu..."

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<div style="font-size:30px">'''MATRIXPRODUCT (a,b,ConsiderUnits)'''</div><br/>
*where <math>a</math> and <math>b</math> 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 <math>a</math> and <math>b</math> is: <math>x_{ij}= \sum_{k=1}^n a_{ik}.b_{kj}</math> where <math>i</math> is the row number and <math>j</math> 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 matrix 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 <math>AB \ne BA </math> (Commutative property)

==Examples==
1. MATRIXPRODUCT([2,3,4;5,6,7],5)
{| class="wikitable"
|-
| 10 || 15 || 20
|-
| 25 || 30 || 35
|}
2. MATRIXPRODUCT([[6,7,8],[10,12,-22],[7,17,23]],[[20,12,16],[7,8,13],[4,8,9]])
{| class="wikitable"
|-
| 120 || 84 || 128
|-
| 70 || 96 || -286
|-
| 28 || 136 || 207
|}

==See Also==
*[[Manuals/calci/MINVERSE | MINVERSE]]
*[[Manuals/calci/MMULT | MMULT]]
*[[Manuals/calci/MDETERM | MDETERM]]

==References==
[http://en.wikipedia.org/wiki/Matrix_multiplication Matrix Multiplication]

*[[Z_API_Functions | List of Main Z Functions]]

*[[ Z3 | Z3 home ]]

@@ Line 34: / Line 34: @@
 | 28 || 136 || 207
 |}
 ==See Also==

Manuals/calci/MATRIXPRODUCT - Revision history

Devika: /* Examples */

Devika: Created page with "'''MATRIXPRODUCT (a,b,ConsiderUnits)''' *where a and b are the array of two matrices ==Description== *This fu..."

Devika: Created page with "
'''MATRIXPRODUCT (a,b,ConsiderUnits)'''

where $a$ and $b$ are the array of two matrices ==Description== This fu..."