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VTU Engineering Maths 1 Nature of the Quadratic form concept easy steps

1,123 views · Published 5 November 2017 · 2:54 · Indexed 22 September 2026

Channel: EASY MATHS EASY TRICKS · 2017 · Education

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In this clip explaining quadratic form conditions, nature and canonical form.This is very easy to understand.
Quadratic forms have many applications in mathematics physics and engineering. In particular they are useful for describing the geometry of conic sections which include circles ellipses parabolas and hyperbolas. The matrix A of a quadratic form can be used to classify conic sections based on the eigenvalues of A. If A has two positive eigenvalues and one negative eigenvalue then the quadratic form corresponds to an elliptical conic section. If A has one positive eigenvalue one negative eigenvalue and one zero eigenvalue, then the quadratic form corresponds to a parabolic conic section. If A has two negative eigenvalues and one positive eigenvalue then the quadratic form corresponds to a hyperbolic conic section.

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