1
vote
2answers
59 views

Linear independence of linear combination of functions

This question is inspired by this question. Is it always true that if $\{f_n(x)\}_n$ are linearly independent then so is $\{f_n(x)+f_n(-x)\}$ given that each $f_n(x)$ do not have definite parity?
0
votes
1answer
74 views

Parity, Set of functions

Given linearly independent $\{f_n\}_{n=1}^N$ how can we form $n$ linearly independent functions $\{F_n\}_{n=1}^N$ such that each $F_n$ is either an even or odd function? Thanks.