Chapter 5 Flashcards
1
Q
Diagonalizable when
A
- If the eigenvalues of A are distinct
- If €dim(Eij) = n
- If the algebraic multiplicity is equal to the geometric multiplicity for every eigenvalue of A
2
Q
Trace
A
Sum of the diagonal elements of A
3
Q
Algebraic multiplicity
A
The multiplicity of lamda as a root of the characteristic polynomial
4
Q
Geometric multiplicity
A
The dimension of the eigenspace of E(llamda)
5
Q
Similar
A
If there exists an invertible matrix C such that B=C^(-1)AC
6
Q
Characteristic equation
A
det(A-(llamda)I)=0
7
Q
Eigenspace
A
The set of Rn consisting of the sub space of Rn generated by the eigenvectors with eigenvalue llamda
