Difference between revisions of "Manuals/calci/DIAGONALMATRIX"

Revision as of 13:32, 8 June 2017

DIAGONALMATRIX(Number)

This function shows the Diagonal matrix of a given order.
In $DIAGONALMATRIX(Number)$ , $Order$ is the order of square matrix.
A diagonal matrix is a square matrix which is of the form $a_{ij}=c_{i}\delta _{ij}$ where $\delta _{ij}$ is the Kronecker delta, $c_{i}$ are constants, and i,j=1, 2, ..., n.
The general diagonal matrix is of the form:

${\begin{bmatrix}c_{1}&0&\cdots &0\\0&c_{2}&\cdots &0\\\vdots &\vdots &\ddots &\vdots \\0&0&\cdots &c_{n}\end{bmatrix}}$

So the main diagonal entries are need not to be zero and off-diagonal entries are zero.
That is,the matrix D = (di,j) with n columns and n rows is diagonal if:

$\forall i,j\in {1,2,....n},i\neq j\Rightarrow d_{i,j}=0$

@@ Line 1: / Line 1: @@
-<div style="font-size:30px">'''DIAGONALMATRIX(Order)'''</div><br/>
+<div style="font-size:30px">'''DIAGONALMATRIX(Number)'''</div><br/>
-*<math>Order</math> is the size or order of the matrix.
+*<math>Number</math> is the size or order of the matrix.
 ==Description==
 *This function shows the Diagonal matrix of a given order.
-*In <math>DIAGONALMATRIX(Order)</math>, <math>Order</math>  is the order of square matrix.
+*In <math>DIAGONALMATRIX(Number)</math>, <math>Order</math>  is the order of square matrix.
 *A diagonal matrix is a square matrix which is of the form <math>a_{ij}=c_{i} \delta_{ij}</math> where <math>\delta_{ij}</math> is the Kronecker delta, <math>c_{i}</math> are constants, and i,j=1, 2, ..., n.
 *The general diagonal matrix is of the form: