Although I am just beginning with Linear Algebra, one thing occurred to me about matrices and vectors. I worried that in my ignorance, I was simply misunderstanding, but maybe not. I stumbled across the following quote and my little thought made sense:
Linear algebra gives you mini-spreadsheets for your math equationshttps://betterexplained.com/articles/linear-algebra-guide/
Now THAT is something I can get on board with! Mini-spreadsheets, sign me up!
I won’t pretend that I actually understand Linear Algebra yet, but I’m more confident than before that I can understand it. Over the years I’ve gradually gained more and more Excel knowledge. In the last 6 months, I’ve learned and applied a lot of new Excel skills, such as Power Query and Goal Seek.
Now that I’ve been given this idea of matrices and vectors being mini-spreadsheets, they should be easier to understand.
For example, once I started thinking about transposing a vector when multiplying it with a matrix, picturing it as a spreadsheet made it much more obvious to me.
If you have a 2 x 2 matrix, like:
And a vector
Knowing to multiply 1 by 5 and 2 by 6 then add them together is kinda complicated to hold in your mind.
But if instead I visualise the vector being transposed and then locking cells, then instead I can say my vector is in C1 and D1 and my matrix begins in A1, I can find my final answer for each number in that matrix is simply the formula:
And then I just drag that down and right!
This would work with matrices and vectors of any size (as long as they match of course).
I’m looking forward to what else I’ll learn in my mini-spreadsheets!