README.md

Dev notes

Can i make this better? yes.
will i do it? nahhh...

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 here.
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 Jul 7, 2024.