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.

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Live on Github Pages here.
Or download Source code directly from here.

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 & Reset Functions:

• three() and two() functions control the visibility of matrix inputs.
• The project uses a responsive Flexbox layout, toggling between matrix modes using CSS classes for a smooth flow.
• Switching between modes automatically triggers clearAll(), which resets all input values and the results area.

2. Matrix Calculation Functions:

2.1 Unified Calculation Logic:

• The project uses a consolidated performCalculation(size) function to handle both 2x2 and 3x3 matrices.
• Input Validation: Since inputs are converted to text fields (to remove browser spin buttons), a custom real-time validator ensures only numeric values (0-9, leading minus, and one decimal point) are accepted.
• Symmetry Check: Determines if the matrix is Symmetric (A = A*) or Non-Symmetric using math.deepEqual().
• Eigensystem: Computes eigenvalues and eigenvectors via math.eigs().
• Diagonalization: Constructs the Modal Matrix $P$, calculates $P^{-1}$, and finally computes $D = P^{-1}AP$.

2.2 Error Handling:

• Smarter error detection specifically identifies if a matrix is non-diagonalizable (when the eigenvectors are not linearly independent) by catching singular matrix errors during the inversion of $P$.

3. Webpage Interaction:

• The layout is now fully responsive, shifting elements to a single column on smaller screens.
• Results are displayed interactively in the textarea with clear, formatted steps.

4. Matrix Operations:

• The code involves operations such as finding determinants, eigenvalues, eigenvectors, matrix transposition, and similarity transformations.

5. External Library:

• The code relies on the math.js library for high-level matrix operations.

In summary, this tool enables users to input 2x2 or 3x3 matrices on a webpage, performs linear algebra operations, and provides a detailed step-by-step diagonalization result.

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.
• Idea of using Textbox (textarea) as an output display in HTML is from LuisBoto's project "JSMatrixCalculator".

Math js

An extensive math library for JavaScript and Node.js. Find it here!.

Last Updated

This README was last updated on April 24, 2026.