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by: Huy Tran

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# Linear Algebra_Week 12: Diagonalization MATH2076

Marketplace > University of Cincinnati > Mathematics (M) > MATH2076 > Linear Algebra_Week 12 Diagonalization
Huy Tran
UC

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-Continue section "eigenvalue and eigenvector" -Concept of diagonal matrix, diagonalizable matrix and step to diagonalize a matrix
COURSE
Linear Algebra
PROF.
TYPE
Class Notes
PAGES
4
WORDS
KARMA
25 ?

## Popular in Mathematics (M)

This 4 page Class Notes was uploaded by Huy Tran on Friday April 8, 2016. The Class Notes belongs to MATH2076 at University of Cincinnati taught by Magda Peligrad in Winter 2016. Since its upload, it has received 19 views. For similar materials see Linear Algebra in Mathematics (M) at University of Cincinnati.

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Date Created: 04/08/16
????1,2 ,…,???????? ????1,????2,…,???????? ????1,????2,…,???? ???? 12 1 4 [2 11 4] 1 3 7 ???????? ???? = 5,10,15 ????????)⃗ 1 7 1 4 1 0 1 ⃗ 2 6 4 ] [0 1 ] 1 3 2 2 0 0 0 1 − 2  ????⃗⃗⃗ ???? [ 1] 3 − 2 1 1 − 1 ???? = 5 [− ] 2 1 3 2 [2] ???? = 10 2 ] ???? = 15 1 1 10 0 0 0 1 0 0 −2 0 0 −5 0 0 [0 −4 0] [ 0 4] [0 0 −7 0 ] 0 0 5 0 0 0 6 ????1 0 0 [ 0 ???? ???? 0 ] 2 0 0 ????3 −2 0 (−2)???? 0 [ 0 4] [ 0 4????] 7 2 [−4 1 ] 1 1 5 0 [−1 −2 ] [0 3 ] [2 1 ] −1 −1 1 1 5???? 0 2 1 [−1 −2][ 0 3????][−1 −1 ] 2.5 − 3???? 5 − 3???? [2.3 − 2.5 2.3 − 5????] × 0 −1 −1 [ 1 2 1] ???? = 0 ???????????? ???? = 1 −1 −1 0   0 −1 −1 [ 1 2 1] −1 −1 0 1 0 −1 [0 1 1] 1 0 0 0  {[−1]} 1  −1 −1 −1 [ ] 1 1 1 −1 −1 −1 −1 −1 −1 [ 0 0 0 ] 0 0 0 −1 −1  {[ 1],[ 0]} 0 1  ???? = 1 1 −1 −1 [−1],[1 ]???????????? [ 0] 1 0 1 ???? ???? ≤ dim(???????????? ???? ) ≤ ???? ????1,????2,…,???? ???? ????????,????????,…,???? ???? ???? ???? 0 0 1 [0 ????2 0 ] [????????,????????,???????? 0 0 ????3 ???? 0 0 3 [0 ????1 0 ] ????????,????????,????????] 0 0 ????2 ????1= 0,???? 2 1,???? 3 1 ???? 0 0 [0 ???? 0] 0 0 ???? 1 −1 −1 ????1 [−1 ] ????2 [ 1 ] ????3 [ 0] 1 0 1 ????2???????????? ???? 3 1 −1 −1 [−1 1 0 ] 1 0 1 1 1 1 [ 1 2 1] −1 −1 0 1 −1 −1 0 0 0 1 1 1 [−1 1 0 ][0 1 0 ][1 2 1] 1 0 1 0 0 1 −1 −1 0

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