CMDA 3606 Study Guide - Midterm Guide: Row And Column Spaces, Scalar Multiplication, Euclidean Vector

• School: Virginia Tech
• Department: Computational Modeling and Data Analytics
• Course: CMDA 3606
• Professor: M Embree

Document Summary

De nitions: orthogonal a notion of perpendicularity in a vector space; two vectors are orthogonal pro- vided vt w = 0, a set of vectors is a subspace if. V for all scalars ir andvectors v (closed under scalar multiplication), and. Ir: linear independence there is no way to write any one of the vectors as a linear combination of the other vectors. In other words, the only way to express. 0 = c1v1 + c2v2 + + cdvd is using the trivial coe cients c1 = c2 = = cd = 0: basis vectors v1, , vd irm for a basis if. Blue box formulas: inner product and norms, best approximation. V = vt w vt v v (1) (2) February 27, 2020: angle between vectors, orthogonal cos 6 (v, w) = If one of the o -diagonal entries of qt q is nonzero, then the columns are not orthogonal.