User Tools

Site Tools


mvg:lecture_02:start

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
Next revision
Previous revision
mvg:lecture_02:start [2018/11/19 12:19] – [Eigenvalue Problem] adminmvg:lecture_02:start [2020/02/04 15:12] (current) – [Eigenvalue Problem] admin
Line 31: Line 31:
 $A\mathbf{v} = \lambda \mathbf{v}$ $A\mathbf{v} = \lambda \mathbf{v}$
  
-$(A-\lambda \unity) A = 0$+$(A-\lambda \one) A = 0$
  
 $\left(A-\lambda \unity \right) A = 0$ $\left(A-\lambda \unity \right) A = 0$
  
 +**Question:**
 +If $P$ is invertible and $B = P^{-1}AP \Rightarrow \sigma(A) = \sigma(B)$. Why?
 +
 +==== Symmetric Matrices ====
 +
 +Real matrix with real Eigenvalues is related to symmetric matrix.
 +
 +$S^T = S$
 +
 +Positive semidefinite: $x^TSx \ge 0$
 +
 +Positive definite: $x^TSx > 0$
 +
 +
 +
 + 
 ==== Vector Spaces, Keywords ==== ==== Vector Spaces, Keywords ====
  
mvg/lecture_02/start.1542629991.txt.gz · Last modified: 2018/11/19 12:19 by admin