find a matrix P that orthogonally diagonalized A and determine
A = (-2, 0, -36 //0,-3,0//-36,0,-23)
my question is: in the process figuring out the P, what the meaning of A is symmetric matrix ?

Question

find a matrix P that orthogonally diagonalized A and determine
A = (-2, 0, -36 //0,-3,0//-36,0,-23)
 my question is: in the process figuring out the P, what the meaning of A is symmetric matrix ?

loser66 · Answer

$$\left[\begin{matrix}-2 & 0&-36 \ 0 & -3&0\-36&0&-23\end{matrix}\right]$$

loser66 · Answer

any idea?

anonymous · Answer

Find the eigenvalues of the matrix by the formula det(A-IR) = 0. Use cofactor expansion to find the characteristic equation, and find the eigenvalues from there. Then, use the eigenvalues to find the eigenvectors, by nil(A-IR)=0. Then, arrange the eigenvalues into a diagonal matrix, and put the corresponding eigenvectors into a matrix to find p.

anonymous · Answer

*sorry, nul(A-IR)=0

anonymous · Answer

I don't have time to solve this problem for you, but that should help

loser66 · Answer

waha, how long your nickname is!!:) 
I know how to manipulate, but my question is above, I ask for benefit we can get from symmetric A

loser66 · Answer

Is it the same with a general matrix? for sure, it's not. but how we use that special property?

caozeyuan · Answer

is this for me? if yes, then I won't learn how to do that until years later！