They’re used for manipulating vectors.
Just like how in
a×v
the a makes the vector v longer or shorter, in
M×v
M can change the vector, for example rotate it.
Just like vectors and other mathematical objects, matrices are purely theoretical concepts. There is no direct real-life meaning to them.
However, there are a bunch of real-world problems where matrices can be put to use to calculate something meaningful.
I fucking loved maths mechanics which is like applied maths/physics. So you’d calculate the distance a ball is thrown or a cannon ball dropped from a cliff. Don’t think we ever did matrices in it though. I enjoyed it so much I’d do excersizes in the book for fun!! That and politics were the only courses I was passionate about.
But I became a software dev that didn’t use maths or politics. :/
So from age 5-17 I hated maths cos I saw no point in it. Until I hit 17 and someone said I can work out how fast a fucking cannon ball travels on impact?! I mean holy dog shit! If someone told me that in primary school I’d have loved maths!
It was very much taught as a means to answer questions though rather than application. So as an adult I’d have to be shown how a number could be found using algebra. But because it wasn’t in an algebra question format it went over my head. It literally required someone taking numbers I’d been given and putting them in a line with letters before my brain engaged to “Oh shit - algebra! I know this!”.
Another example is differentiation. I recently looked up my notes and remembered it was told to us very mechanically: f(x) = 4x^3 => f'(x) = 4(3x^2) = 12x^2
No idea why that’s the case - it just is.
It’s a shame cos I learnt I love maths at 17 but by that point I’d lost years of potential.
P.S. any advice on where I can re-learn real-world maths? I’d love to redo my teens maths learning for fun.
They’re used for manipulating vectors.
Just like how in
a×v
the a makes the vector v longer or shorter, in
M×v
M can change the vector, for example rotate it.
Just like vectors and other mathematical objects, matrices are purely theoretical concepts. There is no direct real-life meaning to them.
However, there are a bunch of real-world problems where matrices can be put to use to calculate something meaningful.
I fucking loved maths mechanics which is like applied maths/physics. So you’d calculate the distance a ball is thrown or a cannon ball dropped from a cliff. Don’t think we ever did matrices in it though. I enjoyed it so much I’d do excersizes in the book for fun!! That and politics were the only courses I was passionate about.
But I became a software dev that didn’t use maths or politics. :/
So from age 5-17 I hated maths cos I saw no point in it. Until I hit 17 and someone said I can work out how fast a fucking cannon ball travels on impact?! I mean holy dog shit! If someone told me that in primary school I’d have loved maths!
It was very much taught as a means to answer questions though rather than application. So as an adult I’d have to be shown how a number could be found using algebra. But because it wasn’t in an algebra question format it went over my head. It literally required someone taking numbers I’d been given and putting them in a line with letters before my brain engaged to “Oh shit - algebra! I know this!”.
Another example is differentiation. I recently looked up my notes and remembered it was told to us very mechanically:
f(x) = 4x^3 => f'(x) = 4(3x^2) = 12x^2No idea why that’s the case - it just is.
It’s a shame cos I learnt I love maths at 17 but by that point I’d lost years of potential.
P.S. any advice on where I can re-learn real-world maths? I’d love to redo my teens maths learning for fun.
I’d like to teach math to anyone who’s interested, but I lack infrastructure to do so, unfortunately.
Zoom+laptop webcam pointed at a sheet of paper?
That doesn’t feel viable.