Alert: this is not an explanatory post of inverse matrix
Back to school when I learned linear algebra, there was always an ultimate question that I asked and I didn’t find an answer: why there is inverse matrix?It seems so simple and so silly and so trivial until I didn’t do well in my final lol.
So why there is a thing called inverse matrix?
Let’s go back to real number system first
reciprocal in real number system Link to heading
Recall in middle school we learned 8*1/8 = 1. Simple enough, right? In order to find what number is reciprocal of 8, we need to do a division 1 divided by 8.
How important is 1 over 8? 1/8 and general representation of this is a powerful tool which I can use to represent how many portion I can divide a thing into. Not only this, but it tells me that number can be instead of integers.
You may feel this is so natural, but is it? How about let’s project this to linear algebra system and revisit?
inverse matrix Link to heading
Let’s say we have a matrix A, we want to know what’s the ‘reciprocal’ of A, how do we do that?
In linear algebra, we couldn’t do 1/A, so we ‘came up with’ inverse of A.
A * inverse of A = I
You may ask what’s the point of inverse of A? You could ask yourself what’s the point of reciprocal in real number system? Now inverse matrix is pretty important is it?
Like you cannot do 1/0 in real number system, not all matrices have inverse matrices, but that’s another topic.
Using inverse matrix, a powerful tool it is, you can quickly find a lot of result matrices.
what’s meaning of an inverse matrix Link to heading
TBC