# Basis Vectors A [basis](https://en.m.wikipedia.org/wiki/Basis_(linear_algebra)) is the set of **building-block vectors** which we can use to represent any other vector in a particular space. Given a [vector space](Abstract%20Vector%20Spaces.md), a set of vectors that span the space is called a basis for the space. For example, for the space of $\mathbb{R}^2$, the two vectors $\begin{bmatrix} 1 \\ 0 \end{bmatrix}$ and $\begin{bmatrix} 0 \\ 1 \end{bmatrix}$ are basis vectors. This essentially means that any vector in $\mathbb{R}^2$ can be expressed as a linear combination of them. ### Intuition A basis is the *lens* that you look at an [Abstract Vector Spaces](Abstract%20Vector%20Spaces.md) through. If you pick a single lens and only look/think through that, you lose the fact that if you took a different lens (basis) you would still be accessing the same underlying structure. So whenever you are working specifically with matrices, you are losing so much structure, because you are including how you think about the space in the definition. You almost lose the fact that there is an underlying structure. --- Date: 20211222 Links to: [Linear Algebra MOC](Linear%20Algebra%20MOC.md) Tags: References: * Math Architectures of Deep Learning (textbook, pg 58)