# Lecture - Linear Algebra MT22, V

> Source: https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/lectures/5/ · Updated: 2022-11-05 · Tags: uni, lecture

### Flashcards
What is the notation for the underlying field in a vector space?::
$$
\mathbb{F}
$$

What is a vector subspace of $V$?::
A non-empty subset $W \subseteq V$ closed under addition and multiplication.

What is the notation for $W$ being a vector subspace of $V$?::
$$
W \le V
$$

How can you write $A$ in terms of the sum of a symmetric and skew-symmetric matrix?::
$$
A = \frac{A + A^\top}{2} + \frac{A - A^\top}{2}
$$

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