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22Apracticefinal

# 22Apracticefinal - Final Review What have we covered since...

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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) 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)) Eigenvalues, eigenvectors, eigenspaces (how to find all of these, what they are good for, diagonalization of linear transformations, theorems) Symmetric matrices (why they are nicer than most matrices, theorems about them) 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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22Apracticefinal - Final Review What have we covered since...

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