- #1
marschmellow
- 49
- 0
I'm sure there are a ton of ways to interpret what the transpose of a matrix represents. Could someone just give me a laundry list of interpretations? Thanks!
I don't think there's a ton of things you can say about transposes in general. But if you know what a specific matrix "does", I'm sure you can figure out what the transpose does. For example, if R rotates a vector in space, then R^{T} is a rotation in the opposite direction.I'm sure there are a ton of ways to interpret what the transpose of a matrix represents. Could someone just give me a laundry list of interpretations? Thanks!
How do you picture the matrix geometrically? It seems that you have to do that before you can picture the difference.Right, I understand the mathematics of it. I just don't understand the interpretation of it. I'm trying to picture the difference between a matrix and its transpose geometrically, but I don't have any insights.
You should try to get over that as soon as possible. Complex matrices are actually easier to deal with than real ones.If the transpose by itself is actually meaningless, and only the adjoint or Hermitian thing has a meaningful interpretation, then I probably don't want to know, because I don't know if my brain can handle the idea of complex quantities on any order higher than scalars.
I don't think there's a ton of things you can say about transposes in general. But if you know what a specific matrix "does", I'm sure you can figure out what the transpose does. For example, if R rotates a vector in space, then R^{T} is a rotation in the opposite direction.
How do you picture the matrix geometrically? It seems that you have to do that before you can picture the difference.
You should try to get over that as soon as possible. Complex matrices are actually easier to deal with than real ones.