The title of this post is an intended homage to two particularly favourite blogs of mine, by fellow students.
Matrices Reloaded
Ramblings of a Short Fat Failed Physicist
Having studied matrices as part of M208 Pure Mathematics, I feel I need a little refresher / revisit / reload of some basic manipulation and applications of them
I have thumbed through several books that I have which cover advanced mathematical physics; and it appears that matrices play a major, prominent role in many areas.
I don't have any particular issues with matrices and I found that Gauss elimination method was one of my best practised methods, as I prepared for the M208 exam.
However, I want to be able to fire through manipulation of matrices, vectors / tensors and other tools, at lightening speed and with pinpoint accuracy. It just feels like it will be nice to have a security blanket going into quantum mechanics and electromagnetism, in February.
Thanks for your kind commendation. I have equally enjoyed yours and Chris's well written and informative blogs and I am always pleased to see a new post. I hope you get on well with your journey into theoretical physics. Matrices do indeed play a role in quantum mechanics - Heisenberg formulated quantum mechanics in terms of matrices in 1925. Recently, I found a 1930 first edition of a translation of his 'The Physical Principles of the Quantum Theory' in a charity shop! I was very pleased to find this.
ReplyDeleteFlattery will get you every where Daniel thanks for the complement. As Duncan says matrices do play an important part in modern physics. As well as the usual stuff the use of matrices in Group theory plays an important part in the classification of vibrational spectra and in classification of particle physics.
ReplyDeleteAlso the concepts eigenvalues and eigenfunctions can be extended to differential operators making a really nice and deep analogy between linear algebra and functions in function space. So yes learn as much linear algebra as possible not just the manipulation but also the abstract stuff. Might be a good idea to revise those bits in M208 now that the exam is over.