## A blank slate

Today, I don’t have any specific thoughts for my blog. This is the empty space, the total void. On the one hand, I have nothing. On the other hand, this is where inspiration strikes.

I suppose I can talk about the null space.

The null space is a mathematical concept that is related to homogeneous linear equations in multiple variables; most specifically, a system of these equations. Now, a homogeneous equation is a linear equation of the form $A _ 1 X _ 1 + A _ 2 X _ 2 + \cdots + A _ n X _ n = 0$. For each linear equation $A _ 1 X _ 1 + A _ 2 X _ 2 + \cdots + A _ n X _ n = B$, there is an associated homogeneous equation, where $B = 0$. So, the null space is the solution to a system of these homogeneous equations; it is a set of values for $X _ 1 , X _ 2 , \cdots , X _ n$ either as actual values or as a system of equations itself, in cases where one term is removed completely. I suppose that statement made no sense.

I’ll update this later and maybe rewrite portions. In any event, welcome to the true work of linear algebra.