- #1
Jason White
- 44
- 1
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?
micromass said: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.
micromass said: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 said: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.
micromass said: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.
Jason White said:I think by proofy he means a class focused on theorems and learning why something is or isn't valid rather than pure application.
"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).Jason White said: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.
Fredrik said:"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).
Matrices are a mathematical tool used to organize and manipulate data or information. In physics, matrices are commonly used to represent and solve systems of equations, transform coordinates, and calculate physical properties such as energy and momentum.
One example is in quantum mechanics, where matrices are used to represent operators such as position, momentum, and energy. These operators act on the wavefunction of a particle and can be used to calculate the probability of finding the particle in a certain state.
Matrices allow us to represent complex physical systems in a compact and organized way. By manipulating and analyzing matrices, we can gain insights into the behavior and relationships of various physical quantities, leading to a better understanding and visualization of the underlying phenomena.
While matrices are a powerful tool, they do have some limitations. For example, they may not be able to accurately represent continuous systems or phenomena with infinite dimensions. In addition, the calculations involving matrices can become computationally intensive for large systems.
A strong understanding of matrices is crucial for physicists, as it allows them to effectively model, analyze, and solve complex physical systems. Matrices are also used in a wide range of other scientific fields, making it a valuable skill for any scientist to have.