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Chapter 8 discusses eigenvectors and eigenvalues of linear maps in finite-dimensional vector spaces, emphasizing the conditions under which a linear map can be diagonalized or tridiagonalized. It defines eigenvalues and eigenvectors, introduces the characteristic polynomial, and explains the relationships between algebraic and geometric multiplicities. The chapter concludes with theorems regarding the representation of linear maps and matrices in upper triangular form based on the nature of their eigenvalue

Author

luytinh

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EN