What does $a_i$ mean in linear algebra?

Question

I'm not understanding what a(sub i)s means in linear algebra. I'm just jumping into linear algebra without many other mathematics experience (Algebra 1, 2, and Geometry)

Also, what is n-vector?

Answer 1

An $n$-vector $a$ is an element of $\mathbf R^n$ or $\mathbf C^n$ (depending on the context) with $n$ entries, say $a=(a_1, \dotsc, a_n)$. Every entry $a_i$, where $i\in \{1, \dotsc, n\}$, is an element of $\mathbf R$ or $\mathbf C$. The $`s`$ means, that all entrys have this property.

Answer 2

The $a_i$s represent the elements in the vector. For example if you have $\begin{align} a &= \begin{bmatrix} a_{1} \\ a_{2} \\ \vdots \\ a_{n} \end{bmatrix} \end{align}$ where $a_1,...,a_n$ are in $\mathbb{R}$ then it could look something like $\begin{align} a &= \begin{bmatrix} 1 \\ 2 \\ \vdots \\ 10 \end{bmatrix} \end{align}$ so $a_1 = 1, a_2 = 2, a_n = 10$

And an $n$-vector is just saying that there are $n$ elements (essentially telling you the size of the matrix). Hope this helps!