33A_review_topics

33A_review_topics - ibility 5. Subspaces, kernel and image...

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MATH 33A Winter 2009 Review Topics 1. Gauss-Jordan elimination, reduced row echelon form, solving systems of linear equations 2. Definition of linear transformations, recognizing linear transformations, matrix of a linear transformation (a) scaling, projection, reflection, rotation 3. Vectors (a) length, dot product, cross product, angle between vectors 4. Matrices (a) matrix multiplication (not commutative), distributive property, inverses, transpose, inverse of product, transpose of product (b) Invertible matrices, invertible transformations, criteria for invert-
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Unformatted text preview: ibility 5. Subspaces, kernel and image of a linear transformation 6. Linearly independent, orthogonal and orthonormal sets of vectors 7. Basis, linear combinations of basis vectors, coordinates, change of basis, similar matrices 8. Gram-Schmidt process for nding an orthonormal basis 9. Determinants, calculating the determinant, geometric interpretation of the determinant, classical adjoint 10. Eigenvalues and eigenvectors, nding them, algebraic vs. geometric multiplicity, diagonalization, powers of a matrix, complex eigenvalues 1...
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This note was uploaded on 04/26/2009 for the course MATH 33a taught by Professor Lee during the Winter '08 term at UCLA.

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