Background Material Linear Algebra Review Linear …

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1Linear Algebra Review and Matlab TutorialLinear Algebra Review and Matlab TutorialAssigned Reading: Eero Simoncelli A Geometric View of Linear Algebra ~eero/ Material A computer vision "encyclopedia": CVonline. Linear Algebra : Eero Simoncelli A Geometric View of Linear Algebra ~eero/ Michael Jordan slightly more in depth Linear Algebra Online Introductory Linear Algebra Book by Jim Hefferon. Standard math textbook notation Scalarsare italic times roman: n, N Vectorsare bold lowercase:x Row vectors are denoted with a transpose:xT Matricesare bold uppercase:M Tensorsare calligraphic letters: TOverview Vectors in R2 Scalar product Outer Product Bases and transformations Inverse Transformations Eigendecomposition Singular Value DecompositionWarm-up: Vectors in Rn We can think of vectors in two ways: Points in a multidimensional space with respect to some coordinate system translation of a point in a multidimensional spaceex.

3 Linear Dependence In R n sets of n+1vectors are always dependent there can be at most n linearly independent vectors Bases (Examples in R2) Bases A basis is a linearly independent set of vectors that spans the “whole space”. ie., we can write every vector in our space as linear combination of vectors in that set.

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