2331_Notes_4o2_fill

2331_Notes_4o2_fill - Math 2331 Linear Algebra Section 4.2...

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Math 2331 Linear Algebra Section 4.2 Orthogonal Projections First, recall the definitions of orthogonal vectors and orthogonal subspaces - Vectors x and y are orthogonal if - Subspaces V and W are orthogonal if 0 vw •= for every v in V and every w in W. - Orthogonal Complements - Definition - The orthogonal complement of a subspace V is the set of all vectors that are orthogonal to all vectors in V. It is denoted V and called "V perp" for short Given an m x n matrix A the orthogonal complements are - Row Space and Null Space and they live in ______ Column Space and Left Null Space and they live in _________ ANY VECTOR IN m \ ANY VECTOR IN n \
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Projections - A 2-D example - Why project? Projection onto a line defined as all multiples of the vector a. Given a vector b and a line defined as all multiples of the vector a, the projection p of b along a is the vector (also sometimes called the projection of b in the direction of a) ± ± T T px a ab a b x aa a a = ==
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Example - Find the projection of the vector
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2331_Notes_4o2_fill - Math 2331 Linear Algebra Section 4.2...

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