Let be A a real \(\displaystyle{N}\times{N}\) matrix

Leia Sullivan

Leia Sullivan

Answered question

2022-04-16

Let be A a real N×N matrix and X a real N×1 matrix.
1. If XTAX=0 and det(A)=0, this implies necessarially that AX=0?
2. If XTAX=0 and det(A)0, exists a condiction to that AX=0 be true?

Answer & Explanation

Latkaxu8j

Latkaxu8j

Beginner2022-04-17Added 11 answers

In both examples below, neither XTA nor AX is zero:
 (110)(100010000)(110)=(110)(110)=0, (11)(1001)(11)=(11)(11)=0.
One obvious sufficient condition that can force AX to be zero whenever XTAX=0 is that A+AT is positive definite, but this has little to do with det(A).

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?