What is the distinction in between matrix concept and also linear algebra?
I have actually raised this from Mathoverflow given that it belongs below.
Currently, I'm taking matrix concept, and also our book is Strang's Linear Algebra. Besides matrix concept, which all designers have to take, there exists linear algebra I and also II for mathematics majors. What is the distinction, if any kind of, in between matrix concept and also linear algebra?
Many thanks! kolistivra
My solution from the MO string :
A matrix is simply a checklist of numbers, and also you're permitted to add and also increase matrices by incorporating those numbers in a particular means. When you speak about matrices, you're permitted to speak about points like the access in the 3rd row and also 4th column, etc. In this setup, matrices serve for standing for points like change chances in a Markov chain, where each access shows the chance of transitioning from one state to an additional. You can do great deals of intriguing mathematical points with matrices, and also these intriguing mathematical points are really vital due to the fact that matrices turn up a whole lot in design and also the scientific researches.
In linear algebra, nonetheless, you rather speak about straight makeovers, which are not (I can not stress this adequate) a checklist of numbers, although occasionally it is hassle-free to make use of a certain matrix to list a straight makeover. The distinction in between a straight makeover and also a matrix is hard to realize the very first time you see it, and also most individuals would certainly be great with merging both perspectives. Nonetheless, when you're offered a straight makeover, you're not permitted to request for points like the access in its 3rd row and also 4th column due to the fact that inquiries like these rely on a selection of basis. Rather, you're just permitted to request for points that do not rely on the basis, such as the ranking, the trace, the component, or the set of eigenvalues. This perspective might appear needlessly limiting, yet it is basic to a much deeper understanding of pure maths.