# Linear-Algebra-MIT-Gilbert-Strang-(L21-L23)

# Lecture 21. Eigen Value and Eigen Vector.

- What a matrix do? It multiplies to a vector, and give out another vector.
**It is like a function.** **The eigenvectors are the vectors that went through the matrix but still remain the same direction.**A*x parallel to x.- Ax = λx, λ can be zero or negative. Ax = 0: Nullspace. X is the eigenvector, λ is the eigenvalue.
- If A is singular, then λ=0 is the eigenvalue.
- Ax=λx, Elimination doesn’t…