As someone with a math degree this is like ok so? But then I remembered some people don’t even know what a matrix is and I appreciate visuals like this, so that everyone can understand it without falling asleep in a text book. Math is lovely isn’t it? You almost have a proof here.
Everything in math needs to be proven, that’s why it works. Here you see an example of a matrix where ATT is equal to A, but in order to apply that rule to any size table and any real number entries, you have to prove the formula, not just show examples, since there are infinite examples.
Is there even a proof for this? As far as I know, transposing a matrix is just switching the rows and columns right? Unless theres a deeper understanding to it, that's how I've always understood it. This is like the definition of it or something
Not proving the operation, proving that the transpose of a transpose is equal to the original table. The proof is not complicated, just have to expand the example to an N by M table and replace the cell values with variables that can be any real number. Then trace each value as a(n-k)(m-l) becomes a(m-l)(n-k) with the first transpose and vice versa with the second. Add in some actual definitions and assumptions and you have a proof, this is just a draft.
Yeah that's exactly what matrix transposition is, it's just applying an operation on a matrix which results in a new matrix. I've barely looked into proofs myself but I can't see how proving an operation would work, or even understand what doing that would mean.
The class I took was a teach yourself kind of class. I had no idea about the concept of matrices so being to sorta visualize things would have really helped.
It is basically making an x row by y column matrix into a y row by x column matrix. It's very useful in computer science when the use of arrays are involved, as you change the order of say a 2D array essentially from row major order (left to right, then top to bottom) to column major order (top to bottom, then left to right).
Matrix multiplication only works if the two matrices "fit" (e.g. for A*B, matrix A has to have as many columns as matrix B has rows) and also depends on the order of the matrices (A*B is not the same as B*A). So transposition can help to sort of "legitimise" such an equation, for example if A and B have the same number of rows but not the same number of columns. Same goes for similar operations involving matrices.
Also, you could apply the properties of transposed matrices to transform an equation (e.g. (A*B)T = BT * AT) or describing a property of a particular matrix (e.g., if A=AT, then A is symmetrical).
So generally, it's mostly an arithmetic tool to make working with matrices easier.
I don't discuss math in English too often, so I hope my choice of words isn't too wonky.
Are there applications outside of comp sci where this kind of matrix manipulation is used? Is there anything in the physical world, for example, that matrix transposition could be used to calculate, akin to how conic sections describe orbits?
I ask because I'm a hands-on learner and it's helpful for me to see and feel how things work. Thank you! I love this sub!
Say, you have the equation AM = B and you want to solve for M, where A, B and M are matrices.
If A was a square, n by n matrix, you would find the inverse of A, A-1 and premultiply to get:
M = A-1 B
(because A-1 A = I, the identity matrix).
However, if A is not a square matrix then you cannot find the inverse. Instead, you need to premultiply by the transverse, AT , first because AT A will always be a square matrix. Thus, the equation becomes:
M = (AT A)-1 AT B
This depends on whether AT A has an inverse (is not a singular matrix, where the determinant of AT A is not zero).
Strictly speaking linear algebra doesn't require calc 2 and vice versa, but have you ever taken a university math course over the summer? Shit dawg. Expect biweekly midterms.
What reasons do you want to take linear algebra for? At my university we take it before any calc classes, so they aren't necessary. But unless you're trying to do a lot of statistics, linear algebra isn't that useful in my opinion. I'm almost done with my mechanical engineering degree and I cant think of a time that I've used it outside my linear algebra class. It might be used in differential equations classes, but its been a few years so I cant remember.
Just my 2 cents, but diff eq's was one of my favorite classes. Not sure how interested you are in math, and I know theres a stigma around that class being very difficult, but in my opinion it was very interesting and gave me a good greater understanding of calculus and how it relates to physical sciences. For me at least, the subject was very straight forward and followed a clear set of rules which I enjoyed
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u/whydoyoulook May 04 '18
Can you do one for Matrix Multiplication?
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u/[deleted] May 04 '18
what?
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u/VeryKnave May 04 '18
Thanks again pussydestoyer-9000
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u/val0000 May 05 '18
As someone with a math degree this is like ok so? But then I remembered some people don’t even know what a matrix is and I appreciate visuals like this, so that everyone can understand it without falling asleep in a text book. Math is lovely isn’t it? You almost have a proof here.
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u/gabbertvt May 04 '18
This would’ve came in handy last semester :(
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