Matrices in Physics - Learn How Math Applies

[Jason White]

I'm learning about Matrix Theory/Linear Algebra and I find this to be pretty interesting in comparison to any other math (calc) I've learned so far. Do matrices get used much in physics?

 

[dx]

Yes, a lot.

 

[Fredrik]

I would say that it's the single most important university-level math topic for physics students, except maybe the most basic stuff about functions, derivatives and integrals from the first calculus course (and high school). Matrices are used in all areas of physics, and are especially important in quantum mechanics.

 

[micromass]

If your course only covers matrix algebra, then it might be worth it to also take a more advanced linear algebra class that covers vector spaces and linear transformations more deeply. I guess that even physics students can benefit from a proofy linear algebra course. It will make QM and GR much easier if you have seen very theoretical linear algebra.

 

[atyy]

I guess that even physics students can benefit from a proofy linear algebra course. It will make QM and GR much easier if you have seen very theoretical linear algebra.

Yes, I think. Being a non-mathematician, I don't really know what a proofy course is, but the abstract structure of linear algebra is far more important for the conceptual understanding of QM than matrix manipulations like SVD.

 

[Arsenic&Lace]

Well, a proofy course and some familiarity with the mathematical machinery/mathematical maturity helps to get an "intuition" for the ideas behind the math of quantum. But the calculation stuff and understanding the theory is pretty handy too; understanding that an operator is diagonal in it's eigenbasis ahead of time, for instance, or knowing the eigenvalue eigenvector problem are both handy skills.

 

[Jason White]

If your course only covers matrix algebra, then it might be worth it to also take a more advanced linear algebra class that covers vector spaces and linear transformations more deeply. I guess that even physics students can benefit from a proofy linear algebra course. It will make QM and GR much easier if you have seen very theoretical linear algebra.

We have learned the basic matrix operations, determinants, inverse matrices, transformations, Vector spaces, subspace, null space, column space, range, kernel etc. We are now doing Bases.

 

[Jason White]

Yes, I think. Being a non-mathematician, I don't really know what a proofy course is, but the abstract structure of linear algebra is far more important for the conceptual understanding of QM than matrix manipulations like SVD.

I think by proofy he means a class focused on theorems and learning why something is or isn't valid rather than pure application. My class is definitely proofy because we need to use the theorems to explain why something is or isn't always consistent etc.

 

[Jason White]

If your course only covers matrix algebra, then it might be worth it to also take a more advanced linear algebra class that covers vector spaces and linear transformations more deeply. I guess that even physics students can benefit from a proofy linear algebra course. It will make QM and GR much easier if you have seen very theoretical linear algebra.

I do plan on taking the next higher level math course which is called Theory of Linear Transformations. The other higher level math courses that have my class (Applied Linear Algebra(Matrix Theory)) as a pre-requisite are classes dealing with linear or non-linear optimization, Topology, probability theory, and maybe one or two more. Whenever i hear optimization i think of the optimization from calculus class and i don't like doing that at all so i probably won't take those classes. And topology and probability theory don't interest me at all.

 

[cochemuacos]

I think by proofy he means a class focused on theorems and learning why something is or isn't valid rather than pure application.

That and doing proofs yourself.

 

[Fredrik]

I do plan on taking the next higher level math course which is called Theory of Linear Transformations. The other higher level math courses that have my class (Applied Linear Algebra(Matrix Theory)) as a pre-requisite are classes dealing with linear or non-linear optimization, Topology, probability theory, and maybe one or two more. Whenever i hear optimization i think of the optimization from calculus class and i don't like doing that at all so i probably won't take those classes. And topology and probability theory don't interest me at all.

"Theory of linear transformations" sounds like exactly what you need. Topology is useful in differential geometry, which you will need to study to get good at general relativity. (Some DG courses have topology as a prerequisite). And it's absolutely essential in functional analysis, which is what you would have to study (in addition to the theory of linear transformations) to really understand the mathematics of quantum mechanics. (Most physicists don't).

 

[micromass]

"Theory of linear transformations" sounds like exactly what you need. Topology is useful in differential geometry, which you will need to study to get good at general relativity. (Some DG courses have topology as a prerequisite). And it's absolutely essential in functional analysis, which is what you would have to study (in addition to the theory of linear transformations) to really understand the mathematics of quantum mechanics. (Most physicists don't).

Of course, differential geometry and functional analysis are only needed if you're really into theory and want to understand the math behind the physics. But "Theory of linear transformations" sounds very useful even if you're not into theory.