- #1
r731
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Let z = [a b]^T be in the 2-dimensional vector space over real numbers, and T a linear transformation on the vector space.
Consider
$$\lim_{z'\rightarrow \mathbf{0}} \frac{T(z+z')-T(z)}{z'}$$
I argue this could be an alternative definition for complex derivative.
To illustrate this, z as a complex number ##a+bi## is a vector [a b]^T and z' is a tiny vector parallel to z. Taking the limit, z+z' approaches z and the limit approaches the rate of change of T at z.
<Moderator's note: please use the proper wrappers, ## ## and $$ $$, for LaTeX.>
Consider
$$\lim_{z'\rightarrow \mathbf{0}} \frac{T(z+z')-T(z)}{z'}$$
I argue this could be an alternative definition for complex derivative.
To illustrate this, z as a complex number ##a+bi## is a vector [a b]^T and z' is a tiny vector parallel to z. Taking the limit, z+z' approaches z and the limit approaches the rate of change of T at z.
<Moderator's note: please use the proper wrappers, ## ## and $$ $$, for LaTeX.>
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