see: multi-variable derivative, gradient, and directional derivative
Multi-Dimensional Derivative and Gradient
Gradient only works for functions that returns one output (
This is exactly the transpose of the gradient:
We can view the multi-variable derivative as a linear transformation acting on a vector, while the gradient is simply a regular vector.
Directional Derivative
The “directional derivative”
where
Different Ways of Thinking
The use of different terminology and different math construct for the same concept demonstrate two different ways of thinking:
vector analysis | linear algebra |
---|---|
directional derivative | rate of change of output |
direction vector | any vector of rates of change of input |
Require | indifferent to lengths and units |