Proving basic results from linear algebra

Asked Dec 17 '15 at 11:14

Active Dec 17 '15 at 13:50

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I had linear algebra a long time ago, and I feel I can do all the computations. However, I still don't know why, for instance, a determinant tells me a system of equations is solvable. I don't know why the determinant gives me the volume of a parallelepipeds.

Most textbooks on linear algebra seem to just skim over this part. The books may tell you why a result is true for the 2x2 matrix, but not the general case.

What book should I read to learn the logic behind concepts like the determinant?

edited Dec 17 '15 at 13:50

Martin Sleziak

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asked Dec 17 '15 at 11:14

Avatrin

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You should try googling it first. What I found. You should change the title of the question as well. It is very misleading. – Dec 17 '15 at 11:17
Wy determinant is volume of parallelepiped in any dimensions and Determinants and volume of parallelotopes. (You can probably find more posts about this.) – Martin Sleziak Dec 17 '15 at 12:00
My question is more general than that. The derminant is an example. Maybe I should edit the question to make that more clear. – Avatrin Dec 17 '15 at 12:03
Maybe it is worth checking some other posts tagged book-recommendation+linear-algebra or reference-request+linear-algebra. – Martin Sleziak Dec 17 '15 at 13:48
You could try Introduction to Linear Algebra by Lang. It carries out the proofs in full in the $2 \times 2$ and $3 \times 3$ cases. For arbitrary $n$, the full proofs are given in his Linear Algebra, but the details might be a bit technical for some people. – David Dec 17 '15 at 14:04

Proving basic results from linear algebra

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