Difference between revisions of "Manuals/calci/IDENTITY"
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| − | <div style="font-size:30px">'''IDENTITY'''</div><br/> | + | <div style="font-size:30px">'''MATRIX("IDENTITY",order)'''</div><br/> |
| + | *<math>order</math> is the order of the Identity matrix. | ||
| + | |||
| + | ==Description== | ||
| + | *This function gives the identity matrix of order 3. | ||
| + | *The matrix is called identity matrix if a square matrix which has a 1 for each element on the main diagonal and 0 for all other elements. | ||
| + | *Identity matrix is denoted by I_n or simply by I. | ||
| + | *Identity matrix is also called as Unit matrix. | ||
| + | *The identity matrix is the identity for matrix multiplication. | ||
| + | *The form of identity matrices are | ||
| + | <math> I_1=\begin{bmatrix} | ||
| + | 1 \\ | ||
| + | \end{bmatrix}</math> | ||
| + | <math>I_2=\begin{bmatrix} | ||
| + | 1 & 0 \\ | ||
| + | 0 & 1 \\ | ||
| + | \end{bmatrix}</math> | ||
| + | <math>I_3=\begin{bmatrix} | ||
| + | 1 & 0 & 0 \\ | ||
| + | 0 & 1 & 0\\ | ||
| + | 0 & 0 & 1 | ||
| + | \end{bmatrix}</math> | ||
| + | ....... | ||
| + | <math>I_n=\begin{bmatrix} | ||
| + | 1 & 0 & 0 & \cdots & 0 \\ | ||
| + | 0 & 1 & 0 & \cdots & 0 \\ | ||
| + | 0 & 0 & 1 & \cdots & 0 \\ | ||
| + | \vdots & \ddots & \vdots \\ | ||
| + | 0 & 0 & 0 & \cdots & 1 | ||
| + | \end{bmatrix}</math> | ||
| + | |||
| + | |||
| + | ==Examples== | ||
| + | *1.MATRIX("identity") = 1 | ||
| + | *2.MATRIX("identity",3) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 1 || 0 || 0 | ||
| + | |- | ||
| + | | 0 || 1 || 0 | ||
| + | |- | ||
| + | | 0|| 0 || 1 | ||
| + | |} | ||
| + | *3.MATRIX("identity",6) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 1 || 0 || 0 || 0 || 0 ||0 | ||
| + | |- | ||
| + | | 0 || 1 || 0 || 0 || 0 || 0 | ||
| + | |- | ||
| + | | 0|| 0 || 1 || 0 || 0 || 0 | ||
| + | |- | ||
| + | | 0 || 0 || 0 || 1 || 0 || 0 | ||
| + | |- | ||
| + | | 0 || 0 || 0 || 0 || 1 || 0 | ||
| + | |- | ||
| + | | 0 || 0 || 0 || 0 || 0 || 1 | ||
| + | |} | ||
| + | |||
| + | ==Related Videos== | ||
| + | |||
| + | {{#ev:youtube|3cnIa0fYJkY|280|center|Identity Matrix}} | ||
| + | |||
| + | ==See Also== | ||
| + | *[[Manuals/calci/HADAMARD| HADAMARD]] | ||
| + | *[[Manuals/calci/HESSENBERG| HESSENBERG]] | ||
| + | *[[Manuals/calci/CIRCULANT| CIRCULANT]] | ||
| + | *[[Manuals/calci/HANKEL| HANKEL]] | ||
| + | |||
| + | ==References== | ||
| + | *[http://en.wikipedia.org/wiki/Identity_matrix Identity Matrix] | ||
Latest revision as of 01:18, 26 October 2015
MATRIX("IDENTITY",order)
- is the order of the Identity matrix.
is the order of the Identity matrix.Description
- This function gives the identity matrix of order 3.
- The matrix is called identity matrix if a square matrix which has a 1 for each element on the main diagonal and 0 for all other elements.
- Identity matrix is denoted by I_n or simply by I.
- Identity matrix is also called as Unit matrix.
- The identity matrix is the identity for matrix multiplication.
- The form of identity matrices are
.......
.......
Examples
- 1.MATRIX("identity") = 1
- 2.MATRIX("identity",3)
| 1 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 1 |
- 3.MATRIX("identity",6)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |