Which Linear Algebra Concepts Are Essential for Physics Majors?

[Crush1986]

I'm a physics major taking Linear Algebra right now. It's been pretty boring but I'm doing well.

I'm just wondering about which concepts from this subject should I really focus on understanding and knowing how to apply well? Obviously I'm focusing on everything and trying to receive and A in the course. I am just curious as to what other physics majors who have been through this have taken from this course as being very valuable.

Thanks in advance to whomever replies and gives me some nuggets of wisdom!

 

[Quantum Defect]

I'm a physics major taking Linear Algebra right now. It's been pretty boring but I'm doing well.

I'm just wondering about which concepts from this subject should I really focus on understanding and knowing how to apply well? Obviously I'm focusing on everything and trying to receive and A in the course. I am just curious as to what other physics majors who have been through this have taken from this course as being very valuable.

Thanks in advance to whomever replies and gives me some nuggets of wisdom!

Linear algebra will be very useful, but many, many of the ideas are most powerfully applied in quantum mechanics.

 

[Crush1986]

Linear algebra will be very useful, but many, many of the ideas are most powerfully applied in quantum mechanics.

Thx for the reply :). Are there any big ideas that you can point out? The biggest one I hear a lot in QM is "Eigen____" Where in the blank goes value, function or state.

 

[Quantum Defect]

Thx for the reply :). Are there any big ideas that you can point out? The biggest one I hear a lot in QM is "Eigen____" Where in the blank goes value, function or state.

In the matrix formulation of qm, you can have large matrices (Hamiltonian) that is written in a convenient basis. You diagonalize the matrix to find the eigenfunctions/vectors (wave functions) and eigenvalues ( energies). The idea of basis functions, vector spaces, etc. pop up all of the time.

 

[Crush1986]

In the matrix formulation of qm, you can have large matrices (Hamiltonian) that is written in a convenient basis. You diagonalize the matrix to find the eigenfunctions/vectors (wave functions) and eigenvalues ( energies). The idea of basis functions, vector spaces, etc. pop up all of the time.

Oh goodie, thx!

 

[micromass]

I think the vast majority of the concepts in linear algebra will turn out to be important. Even more theoretical things like dual spaces are important to understand well.
I think the best thing you can do is to find an easy course on quantum mechanics and to start reading it. The point is not to understand everything in it, of course, but to get some more intuition for what the linear algebra really means physically.

 

[gleem]

Linear algebra also has applications in Mechanics, Geometry, Topology, Relativity, and Electromagnetic Theory