This preview shows pages 1–5. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: of u and another vector z that is orthogonal to u . We usually call y the projection of y onto u . When c 6 = 0, then y is the same as the projection of y onto c u . CHECK THIS! As a result we can think of y as the projection of y onto the subspace (or line) L spanned by u . Consequently we write 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...
View Full
Document
 Spring '08
 PAVLOVIC

Click to edit the document details