How to Find the Adjoint of a Matrix in MATLAB?

MATLAB stands for matrix laboratory and the basic purpose of its development was to efficiently perform complicated matrix operations. One such matrix operation is finding the adjoint of a matrix which can be easily performed on a 2-by-2 matrix; however, it is difficult for matrices having a size greater or equal to 3. This operation can be easily and effectively performed on MATLAB for any square matrix having any large or small size because of the built-in adjoint() function.

This tutorial is going to discover how to determine the adjoint of a matrix in MATLAB.

Why Should We Need to Find an Adjoint of a Matrix

Finding the adjoint of a matrix is necessary especially when you:

Find the Inverse of a Matrix
Solve a System of Linear Equations
Encrypt Message Codes
Trace User Data

How to Find Adjoint of a Matrix in MATLAB

In MATLAB, we can easily find the adjoint of a matrix using the built-in adjoint() function. This function is responsible for finding the adjoint of the given square matrix since it accepts a square matrix as an input and returns the computed adjoint of a matrix as an output.

Syntax
The adjoint() function can be used in MATLAB through the following syntax:

X = adjoint(A)

Here,

The function adjoint(A) is responsible for calculating the adjoint of a given matrix A such that the computed adjoint matrix X satisfies the given equation.

Where n represents the rows of the given matrix A.

Example 1: How to Determine the Adjoint of a Matrix in MATLAB?

This MATLAB code computes the adjoint of the given square matrix having size n=5 created by the magic() function using the adjoint() function.

A = magic(5);
X = adjoint(A)

Example 2: How to Compute Adjoint of a Symbolic Matrix in MATLAB?

In this example, we use the adjoint() function to find the adjoint of the given symbolic matrix in MATLAB.

syms a b c d e f
A = sym([1 a 2; b c d;e 0 f]);
X = adjoint(A)

Conclusion

Manually computing the adjoint of a matrix having size n = 3 or above is a difficult and time-consuming task. However, with MATLAB it can easily be done within seconds due to the built-in adjoint() function that allows you to calculate the adjoint of any square matrix. This guide has provided the importance of finding the adjoint of a matrix, and the use of adjoint() function with examples in MATLAB.