Introduction
The identity matrix is a the simplest nontrivial diagonal matrix, defined such that
1 x (X) = X
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for all vectors x. An identity matrix may be denoted 1,I,E (the latter being an abbreviation for the German term "Einheitsmatrix"; Courant and Hilbert 1989, p. 7), or occasionally , with a subscript sometimes used to indicate the dimension of the matrix. Identity matrices are sometimes also known as unit matrices (Akivis and Goldberg 1972, p. 71).[1]
![I=[1 0 ... 0; 0 1 ... 0; | | ... |; 0 0 ... 1].](https://lh4.googleusercontent.com/vCg5qgQ0DIwy0IA_c14K6pwxYH9PMRFl9wQgbSO1HQHTkTwmbW0xK1TwGjNM_DUs8HxLPJSO-NGDRigOThdEMwojXEYk1n8JT7kKM6vRUL_wV3k8EMIB-jufruw0GB5rWX6hA7gV) |
Image Courtesy: wikipedia.org
Programs:
#include <stdio.h>
#define ID 15
int main(){
int i,j;
int identity=ID+1;
int a[ID][ID];
/*Loop until the user enter's the data correctly */
while(identity>ID){
printf("Enter the value for identity Matrix<%d:", ID);
scanf("%d", &identity);
}
/*Input the value for identity matrix in array */
for(i=0;i<identity;i++){
for(j=0;j<identity;j++){
/* if i=j then the value is always 1 in identity matrix */
if(i==j){
a[i][j]=1;
}
/* if i!=j then the value is always 0 in identity matrix */
else{
a[i][j]=0;
}
}
}
printf("\n");
/* Print the entire identity matrix */
for(i=0;i<identity;i++){
printf("\t|");
for(j=0;j<identity;j++){
printf(" %d ", a[i][j]);
}
printf("|\n");
}
}
#define ID 15
int main(){
int i,j;
int identity=ID+1;
int a[ID][ID];
/*Loop until the user enter's the data correctly */
while(identity>ID){
printf("Enter the value for identity Matrix<%d:", ID);
scanf("%d", &identity);
}
/*Input the value for identity matrix in array */
for(i=0;i<identity;i++){
for(j=0;j<identity;j++){
/* if i=j then the value is always 1 in identity matrix */
if(i==j){
a[i][j]=1;
}
/* if i!=j then the value is always 0 in identity matrix */
else{
a[i][j]=0;
}
}
}
printf("\n");
/* Print the entire identity matrix */
for(i=0;i<identity;i++){
printf("\t|");
for(j=0;j<identity;j++){
printf(" %d ", a[i][j]);
}
printf("|\n");
}
}
Output:
Enter the value for identity Matrix<15:5
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 1 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 1 |
Process returned 5 (0x5) execution time : 4.578 s
Press any key to continue.
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References:
Akivis, M. A. and Goldberg, V. V. An Introduction to Linear Algebra and Tensors. New York: Dover, 1972.
Ayres, F. Jr. Schaum's Outline of Theory and Problems of Matrices. New York: Schaum, p. 10, 1962.
Courant, R. and Hilbert, D. Methods of Mathematical Physics, Vol. 1. New York: Wiley, 1989.
Weisstein, Eric W. "Identity Matrix." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/IdentityMatrix.html
