Linear Space or Vector Space over a field K Definition: The linear space over a field K is a non-empty set along with a function $+ : X \times X \to X$ called linear/vector addition (or just, ‘addition‘) and another function $ \cdot : K \times X \to X$ called

# Norm of a Function

Square Integrable function or quadratically integrable function $\mathfrak{L}_2$ function A function $y(x)$ is said to be square integrable or $\mathfrak{L}_2$ function on the interval $(a,b)$ if $$\displaystyle {\int_a^b} {|y(x)|}^2 dx <\infty$$ or $$\displaystyle {\int_a^b} y(x) \bar{y}(x) dx <\infty$$. For further reading, I suggest this Wikipedia page. $y(x)$ is then also