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Unformatted text preview: Harvard University, Math 20 Fall 2010, Instructor: Rachel Epstein 1 Review sheet 2 1. Vector spaces, bases, and dimension (from supplement) (a) Know the definitions of vector space, basis, and dimension. Be able to identify when something is or is not a vector space, by the definition. (b) Be able to find a basis for a given vector space, and determine the dimension of the space. 2. Eigenvalues, eigenvectors, diagonalization (14.45): (a) Know the definition of eigenvalue and eigenvector, and how to use it. For example, be able to show that if ~v is an eigenvector of A with eigenvalue , then ~v is an eigenvector of A 2 with eigenvalue 2 . (b) Be able to find the characteristic polynomial, all real eigenvalues, eigenspaces, bases for eigenspaces, and algebraic and geometric multiplicities of eigen values. Also be able to find an eigenbasis if one exists. (Note: I will not make you factor any polynomials of degree 3 or higher, but you might have to factor a quadratic polynomial to find eigenvalues, so you should be able to use the quadratic formula.) (c) Be able to find a diagonal matrix...
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 Fall '11
 RachelEpstein
 Math, Vector Space

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