Vector Spaces 3

Question 1

What is notation L(V,W)

Answer 1

Notation L(V,W) is ( phi: V to W s,t phi is linear)

Question 2

When is L(V,W) a vector space under pointwise addition and scalar multiplication

Answer 2

L(V,W) is a vector space under pointwise addition and scalar multiplication when
L(V,W) <= W^V (set of maps V to W)

Question 3

How can a linear map be represented as a matrix

Answer 3

Write phi(Vj) (jth basis vector) in terms of W1,…,W, to set jth column of A)

Question 4

What does v,w E V are congruent module U : v identical w mod U mean

Answer 4

V,w E V congruent modulo U: v identical w mod U means
V - w E U