Difference between revisions of "Manuals/calci/DIAGONALMATRIX"

Revision as of 14:03, 6 June 2017

DIAGONALMATRIX(Order)

This function shows the Diagonal matrix of a given order.
In $DIAGONALMATRIX(Order)$ , $Order$ 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:

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

@@ Line 5: / Line 5: @@
 *This function shows the Diagonal matrix of a given order.
 *In <math>DIAGONALMATRIX(Order)</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.
+*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:
 <math>\begin{bmatrix}
@@ Line 13: / Line 13: @@
 & 0 & \cdots & c_{n}
 \end{bmatrix} </math>
-As stated above, the off-diagonal entries are zero. That is, the matrix A = (ai,j) with n columns and n rows is diagonal if
+*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:
+<math>\forall i,j \epsilon {1,2,....n},i \ne j \rArr d_{i,j} = 0</math>
+<math>\isin</math>