Quadratic Forms → Canonical Form | Complete Guide for Engineering & Mathematics Students

In this video, we learn how to reduce quadratic forms to canonical form in a simple step-by-step way.
First, we write the quadratic form in matrix form using XᵀAX. Then, we use diagonalization with NᵀAN and finally apply the substitution X = NY to get the canonical form.

The method shown here is useful for understanding linear algebra, matrix algebra, and university-level mathematics. It will also help in exam preparation for engineering and science students.

What you will learn in this video:

Converting quadratic forms into matrix form

Writing quadratic forms as XᵀAX

Using diagonalization with NᵀAN

Applying substitution X = NY

Getting the quadratic form into canonical form with clear examples

This tutorial is designed to build a strong understanding of the topic and make the process easy to follow.

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