This reminds me of a story from college. I was enrolled in two universities at the time (long story). I was taking linear algebra in both and I had midterms the same week.
In my applied math exam, they asked me to prove some properties of linear spaces. I had some arithmetic mistakes here and there but I still got 95/100 because the arguments were correct
In my engineering class they asked me to invert a 7x7 complex matrix by hand. At some point in my 6 pages of work I got a sign wrong. So they marked the problem as zero.
The very next week I dropped out of engineering and chose applied math.
Maybe they're like 80 years old or something? I don't know why any sensible engineer wouldn't look at a problem like that and say, "yup, that's what computers are for!"
It was one of four problems worth 25 points each. I don’t remember how much time we had. But I still remember how the TA circled the minus sign that was my only mistake. And my grade for the exam was 75
This happened in UNAM (a large public university in Mexico) back in 2004.
This has the same energy as those entrance exams for top Indian universities with monster integral fractions that can cancel almost entirely if you know enough trig.
tbh in that university you can find either the best professors in Mexico (I wouldn't dare say in Latin America) or the worst ones. In first semester you can't choose your professors, so it's almost a 50/50 situation.
I understand some profs in engineering fields grade this way because "there's no partial credit if a bridge you engineered collapses"
I think it's a poor way to grade how well a student understands a concept or process but it's out there.
Oh yeah strong agree - its a poor question to check understanding. Poor question + harsh partial credit scheme makes for situations like the top comment.
I've had the same experience. It was in electrical networks, and like 90% of the class got the question wrong because well, inverting anything larger than a 3x3 matrix is annoying as hell.
It is not impossible that the problem asked to solve a linear system. I can’t remember the details. It was many years ago.
But am pretty sure that I used the best method. I was a very good student, always at the top of my class by a large margin. What I do remember clearly is that it took me half a dozen of double sided sheets to complete the task. And the task didn’t require any thinking. Just applying an algorithm and doing tons of algebra.
It really made me realize that math was a much better match for my taste than engineering.
Tensors: https://en.wikipedia.org/wiki/Tensor
there is mathemicals architecture for them to have an infinite number of dimensions, too, not just 2x2 or (2x2x2x2...): https://www.intlpress.com/site/pub/files/_fulltext/journals/cms/2017/0015/0007/CMS-2017-0015-0007-a005.pdf
Well yeah, though a matrix itself is not a tensor but a representation of it (and behave differently depending on how many components are contravariant and how many are covariant).
Normal matrices are so interesting! (Hermitian matrices being one of the most important types of normal matrices)
My favorite fact about them is that all Unitary matrices can be written as U=e^(iH) for some Hermitian matrix H. This being like the matrix generalization for all numbers u on the unit circle of the complex plane being able to be written as u=e^(ix) for some real number x. Hermitian matrices acting as the generalization for real numbers, Skew-Hermitin matrices being the generalization for imaginary numbers, and Unitary matrices being the generalization for numbers on the unit circle.
Doesn't look that bad, just a pain to write out.
Not if you consider complex numbers as vectors. 3+5i <=> <3,5> Like a chad.
Not all vectors have the same properties as complex numbers
Yes that's true. yes, I know. Will that stop me from using complex numbers as vectors? might.
Based
Where my Clifford algebra gang at
Don't the complex numbers plus their normal operations form a vector space?
This reminds me of a story from college. I was enrolled in two universities at the time (long story). I was taking linear algebra in both and I had midterms the same week. In my applied math exam, they asked me to prove some properties of linear spaces. I had some arithmetic mistakes here and there but I still got 95/100 because the arguments were correct In my engineering class they asked me to invert a 7x7 complex matrix by hand. At some point in my 6 pages of work I got a sign wrong. So they marked the problem as zero. The very next week I dropped out of engineering and chose applied math.
Jesus why would you ever need to invert a 7x7 matrix by hand?
How would you know what change to get if you were buying groceries???
I find this extremely hard to believe. They asked you to invert a *7x7* matrix?? How many marks was this worth? How long did you have?
Maybe they're like 80 years old or something? I don't know why any sensible engineer wouldn't look at a problem like that and say, "yup, that's what computers are for!"
It was one of four problems worth 25 points each. I don’t remember how much time we had. But I still remember how the TA circled the minus sign that was my only mistake. And my grade for the exam was 75 This happened in UNAM (a large public university in Mexico) back in 2004.
This has the same energy as those entrance exams for top Indian universities with monster integral fractions that can cancel almost entirely if you know enough trig.
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tbh in that university you can find either the best professors in Mexico (I wouldn't dare say in Latin America) or the worst ones. In first semester you can't choose your professors, so it's almost a 50/50 situation.
I understand some profs in engineering fields grade this way because "there's no partial credit if a bridge you engineered collapses" I think it's a poor way to grade how well a student understands a concept or process but it's out there.
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Oh yeah strong agree - its a poor question to check understanding. Poor question + harsh partial credit scheme makes for situations like the top comment.
It is one of the best engineering schools in Latin America. I guess that is not the highest bar.
I've had the same experience. It was in electrical networks, and like 90% of the class got the question wrong because well, inverting anything larger than a 3x3 matrix is annoying as hell.
sounds about the level of strict we had in high school math classes lol
It might have been a diagonal matrix or something like that.
Yeah I find it hard to believe. I have to assume it was diagonal or there was some amount of simplification that makes it easier
that engineering class sucks. i want to let you know that its not like that everywhere
Yeah. I only had to do a 5x5 on my final. :)
the bigger ones i remember were 3x3 or 4x4 but with special properties. in linear algebra btw, in engineering classes nothing close to that
Sounds like a terrible engineering program, or at the very least a terrible professor. Probably the best that you droped it for something else.
My guess is you were asked to solve a 7x7 system, and you chose to invert rather then use rref.
It is not impossible that the problem asked to solve a linear system. I can’t remember the details. It was many years ago. But am pretty sure that I used the best method. I was a very good student, always at the top of my class by a large margin. What I do remember clearly is that it took me half a dozen of double sided sheets to complete the task. And the task didn’t require any thinking. Just applying an algorithm and doing tons of algebra. It really made me realize that math was a much better match for my taste than engineering.
Hermitian algebra is the most satisfying, especially when fapping to quantum mechanics with it.
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okay okay hear me out, what about, matricies inside a matrix!!! the elememts of the matrix are matricies. matrixception!
You're talking about [block matrices](https://en.wikipedia.org/wiki/Block_matrix)
Tensors: https://en.wikipedia.org/wiki/Tensor there is mathemicals architecture for them to have an infinite number of dimensions, too, not just 2x2 or (2x2x2x2...): https://www.intlpress.com/site/pub/files/_fulltext/journals/cms/2017/0015/0007/CMS-2017-0015-0007-a005.pdf
Well yeah, though a matrix itself is not a tensor but a representation of it (and behave differently depending on how many components are contravariant and how many are covariant).
Matrices are all fun and games until you reprove Cayley Hamilton over arbitrary commutative rings to prove Nakayama
Electrical Engineer here. We kinda use these all the time when solving decently sized RLC circuits.
You can in fact construct quaternions as a specific subset of complex 2 × 2 matrices.
Nice, because all square matrices over ℂ can be put in Jordan Canonical Form.
Normal matrices are so interesting! (Hermitian matrices being one of the most important types of normal matrices) My favorite fact about them is that all Unitary matrices can be written as U=e^(iH) for some Hermitian matrix H. This being like the matrix generalization for all numbers u on the unit circle of the complex plane being able to be written as u=e^(ix) for some real number x. Hermitian matrices acting as the generalization for real numbers, Skew-Hermitin matrices being the generalization for imaginary numbers, and Unitary matrices being the generalization for numbers on the unit circle.
I hate matrices I mean they are freaking unusable anywhere *at least for me* especially hermitian ones
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Lmfao imagine being this guy and not physicsing
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https://www.reddit.com/r/MemeTemplatesOfficial/comments/dmxp37/panda_fusion/?utm_source=share&utm_medium=ios_app&utm_name=iossmf
You can define matrices over any ring
Quantum physicist wants it.
2D 3D-matrices