How to find a standard matrix for a transformation?
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How could you find a standard matrix for a transformation T : R2 → R3 (a linear transformation) for which T([v1,v2]) = [v1,v2,v3] and T([v3,v4-10) = [v5,v6-10,v7] for a given v1,...,v7? I have been thinking about using a function but do not think this is the most efficient way to solve this question. Could anyone help me out here? Thanks in advance. Walter
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Jan
le 4 Oct 2017
Using a function or not is not the question here. It does not matter if you calculate this in a function or directly in the code.
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Roger Stafford
le 4 Oct 2017
Assuming the transformation is homogeneous - that is, it leaves the origin fixed - what you have here is six linear equations with six unknown coefficients. Just use standard matlab methods for solving them.
If the transformation is not necessarily homogeneous, then you don’t have enough information for a solution. You would need three instead of the two equalities above.
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Roger Stafford
le 5 Oct 2017
Yes, Matt, you are right. This is a difference between linear transformations and linear equations.
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