Linear Algebra and Its Applications · Problem 6.2.25

Positive Definite Matrices — Gilbert Strang

Mathematics · tests-for-positive-definiteness

Problem

You may have seen the equation for an ellipse as

\left(\frac{x}{a}\right)^2 + \left(\frac{y}{b}\right)^2 = 1

. What are

a

and

b

when the equation is written as

\lambda_1 x^2 + \lambda_2 y^2 = 1

? The ellipse

9x^2 + 16y^2 = 1

has half-axes with lengths

a = \underline{\quad}

, and

b = \underline{\quad}