Timeline for What is the difference between matrix theory and linear algebra?
Current License: CC BY-SA 2.5
6 events
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| Aug 4, 2010 at 5:36 | comment | added | Per Vognsen | Belated comment: Depends on what you call a matrix, Harry. If $X$ and $Y$ are sets and $K[X]$ and $K[Y]$ are their free K-vector spaces then a linear map $\colon K[X] \to K[Y]$ is the same as a map of sets $X \to K^Y = X \times Y \to K$. I'd argue this is what a matrix really is and that ordering is an artifact of trying to write something in linear order on a piece of paper. | |
| Mar 30, 2010 at 22:30 | comment | added | Harry Gindi | Even worse, matrices depend on a choice of an ordered basis. | |
| Jan 14, 2010 at 15:00 | comment | added | abcdxyz | An even more basic question but in the same line is "What is the difference of a vector and a row (collum) matrix".Vectors are mathematical object living in a linear space or vector space (which satisfy certain properties). Choosing a special set of vectors called a base, we can decompose every vector in the vector space into a kind of sum of vectors in this base. Thus every vector in a code, and this is the row (collum) matrix. The next step is to look at the homomorphisms (maps) between linear spaces. Choosing the base of the domain and the range we can represent the homomorphism by a matrix | |
| Jan 14, 2010 at 1:49 | vote | accept | kolistivra | ||
| Jan 13, 2010 at 23:44 | comment | added | Dan Piponi | While it is true that people doing "Matrix Theory" often spend a lot of time with a choice of basis, it's important to note that this is frequently in pursuit of quantities that are invariant of choice of basis. | |
| Jan 13, 2010 at 18:29 | history | answered | Qiaochu Yuan | CC BY-SA 2.5 |