This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
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 ex-actly 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...
View Full Document