16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 8.2.4
Inner Product Spaces
Mathematics — Linear Algebra · distance-inner-product
Problem
Let V be an inner product space. The distance between two vectors α and β in V is defined by
d(α,β)=∥α−β∥.
Show that
(a) d(α,β)≥0;
(b) d(α,β)=0 if and only if α=β;
(c) d(α,β)=d(β,α);
(d) d(α,β)≤d(α,γ)+d(γ,β).