Question

Which among the following is not a type of quadratic form?

(a) Positive Semi-definite

(b) Negative definite

(c) Partial definite

(d) Indefinite

The question was asked during an interview.

My question is based upon Canonical Form or Sum of Squares Form topic in portion Eigen Values and Eigen Vectors of Engineering Mathematics

Answer 1

Right choice is (c) Partial definite

For explanation I would say: Quadratic forms can be classified based on the nature of the eigen values of the matrix into 5 types:

i. Positive definite

ii. Negative definite

iii. Positive Semi-definite

iv. Negative Semi-definite

v. Indefinite