Difference between revisions of "Manuals/calci/MATRIXPOWER"
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(Created page with "<div style="font-size:30px">'''MATRIXPOWER (a,b,ConsiderUnits)'''</div><br/> *<math>a </math> is any matrix. *<math> b</math> is any constant value or any matrix. ==Descripti...") |
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*So it is finding the power value of first value in the first matrix to the power first value in the second matrix. | *So it is finding the power value of first value in the first matrix to the power first value in the second matrix. | ||
*Consider 3x3 matrices with the entries <math>A=(a_{ij})</math> and <math>B=(b_{ij})</math>,i and j= 1,2,3. | *Consider 3x3 matrices with the entries <math>A=(a_{ij})</math> and <math>B=(b_{ij})</math>,i and j= 1,2,3. | ||
| − | *So it is calculating <math>a_{11}^{b_{11}}</math>,<math>a_{12}^{b_{12}}</math> | + | *So it is calculating <math>a_{11}^{b_{11}}</math>,<math>a_{12}^{b_{12}}</math> and <math>a_{13}^{b_{13}}</math> |
*Suppose second matrix is less column or row values then the power value will assigned as 0. | *Suppose second matrix is less column or row values then the power value will assigned as 0. | ||
*After calculating power value the remaining row and column values will display as 1. | *After calculating power value the remaining row and column values will display as 1. | ||
| + | |||
| + | ==Examples== | ||
| + | 1. MATRIXPOWER([2,3,4;5,6,7],5) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 32 || 243 || 1024 | ||
| + | |- | ||
| + | | 3125 || 7776 || 16807 | ||
| + | |} | ||
| + | 2. MATRIXPOWER([3,4,9;10,12,7;5,4,8],[5,2,7;3,6,9;11,12,13]) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 243 || 16 || 4782969 | ||
| + | |- | ||
| + | | 1000 || 2985984 || 40353607 | ||
| + | |- | ||
| + | | 48828125 || 16777216 || 549755813888 | ||
| + | |} | ||
| + | |||
| + | |||
| + | ==See Also== | ||
| + | *[[Manuals/calci/MATRIXEXP| MATRIXEXP]] | ||
| + | *[[Manuals/calci/MATRIXOPERATORS| MATRIXOPERATORS]] | ||
| + | *[[Manuals/calci/MATRIXMOD| MATRIXMOD ]] | ||
| + | |||
| + | ==References== | ||
| + | *[http://mathworld.wolfram.com/MatrixPower.html Matrix Power] | ||
| + | |||
| + | *[[Z_API_Functions | List of Main Z Functions]] | ||
| + | *[[ Z3 | Z3 home ]] | ||
Revision as of 16:14, 21 June 2017
MATRIXPOWER (a,b,ConsiderUnits)
- is any matrix.
- is any constant value or any matrix.
is any matrix.
is any constant value or any matrix.Description
- This function shows the power value of all the corresponding entries.
- In , and are any two matrices.
- The power of a number indicating how many times we have to multiply the number.
- Power is also called Exponents or Indices.
- Here both matrices should be the same dimension.
- So it is finding the power value of first value in the first matrix to the power first value in the second matrix.
- Consider 3x3 matrices with the entries and ,i and j= 1,2,3.
- So it is calculating , and
- Suppose second matrix is less column or row values then the power value will assigned as 0.
- After calculating power value the remaining row and column values will display as 1.
, 
and 
,i and j= 1,2,3.
,
and 
Examples
1. MATRIXPOWER([2,3,4;5,6,7],5)
| 32 | 243 | 1024 |
| 3125 | 7776 | 16807 |
2. MATRIXPOWER([3,4,9;10,12,7;5,4,8],[5,2,7;3,6,9;11,12,13])
| 243 | 16 | 4782969 |
| 1000 | 2985984 | 40353607 |
| 48828125 | 16777216 | 549755813888 |