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Unformatted text preview: of u and another vector z that is orthogonal to u . We usually call ˆ y the projection of y onto u . When c 6 = 0, then ˆ y is the same as the projection of y onto c u . CHECK THIS! As a result we can think of ˆ y as the projection of y onto the subspace (or line) L spanned by u . Consequently we write ˆ y = proj u y = proj L y = y · u u · u u . EXAMPLE. Compute the orthogonal projection of " 3 5 # onto the line through "1 2 # as well as the distance from " 3 5 # to this line. FACT 3. An m × n matrix U has orthonormal columns exactly when U T U = I . FACT 4. Multiplying vectors by matrices whose columns are orthonormal preserves lengths, dot products, and orthogonality. ORTHOGONAL MATRICES. An orthogonal matrix is a square matrix whose inverse is its transpose. HOMEWORK: SECTION 6.2...
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This note was uploaded on 03/06/2010 for the course M 340L taught by Professor Pavlovic during the Spring '08 term at University of Texas.
 Spring '08
 PAVLOVIC

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