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Unformatted text preview: the two vectors. This implies that two nonzero vectors are perpendicular or orthogonal exactly when their dot product is 0. THE PYTHAGOREAN THEOREM. Two vectors u and v are orthogonal exactly when  u + v  2 =  u  2 +  v  2 . DRAW A PICTURE AND CALCULATE. If W is a subspace of R n and if the vector x in R n is orthogonal to every vector in W , then we say that x is orthogonal to W . The set of all vectors orthogonal to W is called the orthogonal complement of W and is denoted by W . FACTS ABOUT ORTHOGONAL COMPLEMENTS. (1) A vector x is in W exactly when x is orthogonal to every vector in a set that spans W . (2) W is a subspace of R n . (3) (Row A ) = Nul A and (Col A ) = Nul A T . HOMEWORK: SECTION 6.1...
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This note was uploaded on 04/15/2008 for the course M 340L taught by Professor Pavlovic during the Spring '08 term at University of Texas at Austin.
 Spring '08
 PAVLOVIC
 Linear Algebra, Algebra, Vectors, Dot Product

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