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Elementary Spanish

by: Johnpaul Bradtke

Elementary Spanish SPAN 1

Johnpaul Bradtke
GPA 3.55


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Class Notes
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This 1 page Class Notes was uploaded by Johnpaul Bradtke on Friday September 4, 2015. The Class Notes belongs to SPAN 1 at University of California - Los Angeles taught by Staff in Fall. Since its upload, it has received 19 views. For similar materials see /class/177791/span-1-university-of-california-los-angeles in Spanish at University of California - Los Angeles.


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Date Created: 09/04/15
If we consider only REAL eigenvalues up to 74 7 then we have the following conclusions about diagonalization 1 An 71 gtlt 71 matrix A is diagonalizable if and only if there exists an eigenspace for A if and only if the dimensions of eigenspaces add up to n a Examples of diagonalizable matrices 26 2 1 0 6 iA 0313 7A272737E25pan 0 7 1 7E3span 1 00 2 0 7 0 The dimensions of eigenspaces add up to 3 See the note for Monday7s 3308 lecture Any 71 gtlt 71 matrix which has distinct real eigenvalues is diagonalizable This is true because the dimensions ofthe eigenspaces add up to 71 Each eigenspace has dimension 17 because geometric multiplicity S algebraic multiplicity 1 in this case A For example 2 6 8 A 0 3 1 0 0 1 A 27 37 1 this is again an triangular matrix One can certainly nd ex amples of matrices which are no triangular For example7 A 4 T b Examples of matrices which are NOT diagonalizable 2 6 2 1 6 i A 0 3 73 7 A 272737 E2 span 0 7 E3 span 1 See the 0 0 2 0 0 note for Monday7s 3308 lecture The dimensions of the eigenspaces add up to 2 There is no eigenbasis for A Therefore7 0 ii A a 7 detA 7 A12 A2 a2 7 A has no real eigenvalue The 710 dimensions of the eigenspaces add up to 0


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