laqf07f_sg_Chap_6 - Linear Algebra Fall...

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Linear Algebra, Fall 2007 (http://www.math.nthu.edu.tw/˜ wangwc/) Study Guide for Chapter 6 1. Section 6.1: (a) Study how to find the eigenvalues and eigenvectors of a square matrix. (b) Remember an example of a real matrix with complex eigenvalues and eigenvectors. (c) Find and remember an example of a 2 × 2 matrix with multiple eigenvalue and more than one linear independent eigenvector. (d) Find and remember an example of a 2 × 2 matrix with multiple eigenvalue and only one linear independent eigenvector. (e) Skip Applications 1, 2. (f) Study the relation between eigenvalues and trace, determinant of a matrix. (g) Study the relation between eigenvalues of similar matrices. 2. Section 6.3: (a) Remember that, not all matrices are diagonalizable. (b) Find and remember an example of 2 × 2 matrix that is not diagonalizable. (c) Study how to diagonalize a matrix and how to find an ’eigenbasis’ of a matrix, whenever possible. (d) Study how to compute A k and A - 1 for a diagonalizable matrix A . (e) Read and study Application 1. (f) Skip Application 2,3. 3. For those who are interested in Section 6.2 and ’The exponential of a matrix’ part of
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