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Does this mean that every possible function from R^m to R^n satisfying the properties on the previous slide must have this form? I haven't thought about this much, but it seems non-obvious.


Is the second statement that a map is linear if it can be expressed as the sum of fixed vectors true in the opposite direction?


how do you map this new vector back to the original?


Can you map the new vector in the new space to the old vector? Does it depend on which spaces we are mapping in between?


What are a1, a2, ..., am here? Are they subject to any constraints?