What is the meaning of matrix eigenvector?

Question

Mathematics

Hello everyone, please explain what is the meaning of the matrix eigenvector ? Whatever linear transformation we apply to such a vector, we will end up with just a collinear vector, just as far as I understand, any vector that we can get through a linear transformation, we can express through eigenvectors (if this is not the case, then correct) ... but what is it for and where can it be needed?

Answer 1

For starters, we could google the following terms: Eigenvector Eigenvalue
Characteristic
polynomial
Nil layers
Nile of
space kjBOesZCoqc&list=P...

Answer 2

Would you like to retell a linear algebra course? Take books ( Ilyin, Kim Linal and angem ) and read until enlightenment.