Final Review
What have we covered since the last midterm? Lots of big, important ideas.
Most of them have to do with assigning or changing a basis to a vector space.
•
Bases (what is a basis, how to check if something is a basis, how to change
basis, what “coordinates” of a vector are with respect to some basis, the
orems about bases)
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Matrix for a linear transformation (how can we represent linear transfor
mations as matrices with respect to some basis, how matrices of a linear
transformation with respect to different bases are related, (i.e., similarity))
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Eigenvalues, eigenvectors, eigenspaces (how to find all of these, what they
are good for, diagonalization of linear transformations, theorems)
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Symmetric matrices (why they are nicer than most matrices, theorems
about them)
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Orthonormal bases (why they are nicer than most bases, theorems about
them)
•
Kernel, image, nullity, rank (what they are, theorems about them, how to
find them)
•
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 Spring '10
 Pon
 Linear Algebra, Vector Space, basis

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