Inverting a matrix is an advanced interview topic. Today, I am going to explain the steps to reverse a matrix or flip a matrix in C#.
Greetings, Interview Preparation Enthusiasts! Today, we're delving into the realm of matrix inversion, a fundamental concept in linear algebra with significant applications in engineering, physics, and computer science. Join us as we thoroughly examine matrix inversion, accompanied by a practical C# implementation example designed to help you tackle your upcoming coding challenges.
Recommended Interview Programs:
C++ Interview Questions for Beginners Most Asked Topics Part 1
What To Understand Star Pattern ? , Search in 2D matrix leetcode program solution,
how to merge two json objects or files,
what is parameter in coding and what is the deference between param and argument in programming
Method Overloading vs. Method Overriding in C#
public static double[,] InvertMatrix(double[,] matrix)
{
int n = matrix.GetLength(0);
double[,] augmented = new double[n, n * 2];
// Initialize augmented matrix with the input matrix and the identity matrix
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
augmented[i, j] = matrix[i, j];
augmented[i, j + n] = (i == j) ? 1 : 0;
}
}
// Apply Gaussian elimination
for (int i = 0; i < n; i++)
{
int pivotRow = i;
for (int j = i + 1; j < n; j++)
{
if (Math.Abs(augmented[j, i]) > Math.Abs(augmented[pivotRow, i]))
{
pivotRow = j;
}
}
if (pivotRow != i)
{
for (int k = 0; k < 2 * n; k++)
{
double temp = augmented[i, k];
augmented[i, k] = augmented[pivotRow, k];
augmented[pivotRow, k] = temp;
}
}
if (Math.Abs(augmented[i, i]) < 1e-10)
{
return null;
}
double pivot = augmented[i, i];
for (int j = 0; j < 2 * n; j++)
{
augmented[i, j] /= pivot;
}
for (int j = 0; j < n; j++)
{
if (j != i)
{
double factor = augmented[j, i];
for (int k = 0; k < 2 * n; k++)
{
augmented[j, k] -= factor * augmented[i, k];
}
}
}
}
double[,] result = new double[n, n];
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
result[i, j] = augmented[i, j + n];
}
}
return result;
}
Step 1 : Matrix Initialization
Initialize the matrix as a 2D array.
Example: A 4x4 matrix with predefined values.
Step 2 : Augmented Matrix Setup
Create an augmented matrix combining the original matrix with an identity matrix.
Example: The left half is the original matrix, and the right half is the identity matrix.
Step 3 : Gaussian Elimination Process
Transform the matrix to its reduced row echelon form by selecting the pivot element and swapping rows if necessary.
Example: Ensure the pivot element is the largest absolute value in the column.
Step 4 : Row Normalization
Normalize the pivot row so that the pivot element becomes 1.
Example: Divide each element of the pivot row by the pivot element.
Step 5 : Column Elimination
Eliminate the other entries in the current column to zero out elements above and below the pivot.
Example: Subtract the appropriate multiple of the pivot row from each other row.
Step 6 : Extracting and Returning the Inverse
Extract the inverse matrix from the augmented matrix.
Example: Copy the right half of the augmented matrix into a separate matrix for the inverse.