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Mar
16
comment Proving properties of linear maps on one-dimensional vectors
@GitGud: Ah, I get it
Mar
16
comment Proving properties of linear maps on one-dimensional vectors
Why do you need the Span condition at all? I also don't understand the second $\iff$
Mar
16
awarded  Commentator
Mar
16
comment Proving properties of linear maps on one-dimensional vectors
@GitGud: still don't follow how you get $Tv = av$? Is there a constructive way to derive that $a$ based on $T$ and the fact that the basis is one-dimensional?
Mar
16
comment Proving properties of linear maps on one-dimensional vectors
@GitGud: an obvious basis for $R^{n}$ is $((1,0,0,...,0),(0,1,0,...,0), ...)$ for $n$ lists (i.e. 0 in all places except the $n$th). You can assume any basis for $R^{n}$ that you'd like though; not sure how this affects the question?
Mar
16
revised Proving properties of linear maps on one-dimensional vectors
added 11 characters in body
Mar
16
comment Proving properties of linear maps on one-dimensional vectors
@GitGud: updated my question to answer this
Mar
16
asked Proving properties of linear maps on one-dimensional vectors
Mar
16
awarded  Promoter
Mar
16
accepted exponential population growth models using $e$?
Mar
15
comment How to define conditions under which linear maps are injective?
@Unwisdom: linear algebra describes solutions to linear equations though and in case of two equations, the solutions are where the two lines intersect, so the equations are definitively of form $f(x) = mx + b$. can you explain the connection between linear maps and this? Why bother with the special case of linear maps as opposed to linear functions? I think I am missing the relevance of linear maps
Mar
6
comment How to define conditions under which linear maps are injective?
What is a linear map intuitively then (e.g. in 2d space) if not a linear function? It seems like an odd concept
Mar
6
comment How to define conditions under which linear maps are injective?
So linear map and linear function are not interchangeable?
Mar
6
asked How to define conditions under which linear maps are injective?
Feb
28
awarded  Tumbleweed
Feb
21
awarded  Scholar
Feb
21
accepted intuition for matrix multiplication not being commutative
Feb
21
asked connection between PCA and linear regression
Feb
17
comment intuition for matrix multiplication not being commutative
@Ted: Can you point to a reference that elaborates on the connection, and makes it obvious that matrices are linear functions?
Feb
17
comment intuition for matrix multiplication not being commutative
thanks, but how does my formulation of linear combinations work when you have $row \times column$ instead of $column \times row$?