your tangent is a line, but your graph shows a curve. Tangent Line is defined as mx+c where m is the slope and c is a constant.
Revisiting this chapter, I remember being confused by the orientation of the gradients listed in section 2.4.3 – as a hint for other readers, I recommend reading the Layout conventions section of the Matrix calculus Wikipedia Article. This textbook’s appendix, specifically section 22.4.7 is also a great resource.
To summarize, there are two popular conventions for vector-vector derivatives:
- In the numerator-based layout (sometimes called the Jacobian layout), the derivative has the same number of rows as the numerator’s dimensionality.
- In denominator-based layouts (sometimes called the Hessian or gradient layout), the derivative has the same number of rows as the denominator’s dimensionality. This is sometimes notated by using a gradient symbol, as the authors do here. You also sometimes see a transpose symbol in the denominator to hint the reader that the denominator-based layout is being used.
This seems to be an error.
should be
.
I have created an issue to talk about this
In 2.4.10, is $$\mathbf A$$ the Jacobian?