Diagonalisation Of Matrix

Diagonalisation of a matrix is the process of reduction of a matrix to diagonal form. The process of reduction of a matrix to diagonal form is as follows: A square matrix of order n with n linearly independent eigen vectors can be diagonalised by a similarity transformations D = (B-)AB where B is the modal matrix whose columns are the eigen vecors of the matrix and (B-) is the inverse of B.

Try It!

Live on Github Pages https://subash2309.github.io/Diagonalisation-of-matrix/
Or download Source code directly form here.

License

This project is licensed under The MIT License.

How it Works?

Note: The diagonalised form of a symmetric matrix (D) can also be obtained using the formula used for skew-symmetric matrix i.e. [(B-)AB]. Therefore, using a normalised matrix may not always be necessary.

1. Matrix Visibility Functions:

• three() and two() functions control the visibility of matrix elements on a webpage.
• For a 3x3 matrix, it makes the elements visible and hides the elements of a 2x2 matrix, and vice versa.

2. Matrix Calculation Functions:

2.1 calculate2() Function (for 2x2 matrices):

• Reads input values from HTML input elements representing a 2x2 matrix.
• Calculates the determinant of the matrix (twdet variable).
• Computes eigenvalues and eigenvectors using the math.eigs() function.
• Determines if the matrix is symmetric or skew-symmetric.
• Calculates the inverse of the eigenvectors and diagonalizes the matrix.
• Displays the results in the console and updates the webpage with the results.

2.2 calculate3() Function (for 3x3 matrices):

• Similar to calculate2(), but for 3x3 matrices.
• Reads input values from HTML input elements representing a 3x3 matrix.
• Calculates the determinant, eigenvalues, and eigenvectors.
• Determines if the matrix is symmetric or skew-symmetric.
• Calculates the inverse of the eigenvectors and diagonalizes the matrix.
• Displays the results in the console and updates the webpage with the results.

3. Webpage Interaction:

• The visibility functions (three() and two()) manipulate the visibility of matrix elements on the webpage.
• The calculated results are displayed in an output box on the webpage, particularly in an HTML element with the ID textarea.

4. Console Logging:

• There are numerous console.log statements for debugging purposes, helping developers understand the intermediate values and steps in the calculations.

5. Matrix Operations:

• The code involves operations such as finding determinants, eigenvalues, eigenvectors, matrix transposition, matrix types (symmetric or skew-symmetric), and diagonalization.

6. External Library:

• The code relies on an external library named math (math.js) for mathematical

In summary, this code enables users to input 2x2 or 3x3 matrices on a webpage, performs various linear algebra operations on them, and displays the results interactively.

References and Credits:

• Understanding of diagonalization of matix in linear algebra Chapter 13 by Weijie Chen.
• Idea and some parts of code for Matrix Selection is from ElenaChes's "JavaScript-HTML-Matrix-Calculator". Check out his/her's project on matrix determinant (solution) calculator.
• Website design inspo and some styles form John doe. Here's his toutrial and the website preview.
• Idea of using Textbox(textarea) as a output display in html is from LuisBoto's poject "JSMatrixCalculator".

Math js

An extensive math library for JavaScript and Node.js. you can find it here!.

math.round()
math.eigs() //for Eigen values and Eigen vectors
math.transpose() //to find the transpose of matrix
math.det() //to find the determinant of matrix
math.inv() //to find the inverse of matrix
math.multiply() //to multiply matrices

Last Updated

This README was last updated on Dec 18, 2023.