# Thread: Help with Positive Definite Proof

1. ## Help with Positive Definite Proof

Problem: Let A and B be symmetric nxn matrices whose eigenvalues are all positive. Show that the eigenvalues of A + B are all positive.

I really don't know where to begin, a hint would be greatly appreciated.

2. Originally Posted by crymorenoobs
Problem: Let A and B be symmetric nxn matrices whose eigenvalues are all positive. Show that the eigenvalues of A + B are all positive.

I really don't know where to begin, a hint would be greatly appreciated.
What machinery do you have to work with?

3. Well, the rest of the questions were about Quadratic forms and their corresponding symmetric matrices, but I don't see that helping me on this proof.

I had to prove that Q is positive definite if Det(A) > 0 and A11 > 0 for the corresponding 2x2 matrix in the previous question.

Should I be checking if det(A+B) > 0 and A11 + B11 > 0 in this question?
If so, how can I go about checking the determinant of an arbitrary sized square matrix without lots of excessive writing.