mikexcohen / linalg4datascience Goto Github PK

Hi, I can't find the file when I download the zip folder. There's only a READM.md. Is that what I should be able to use?

Screenshot

Wrong iterating variable in the nested for loop. y is used as an iterator as well as an iterated sequence. So after this loop, y is just a scalar(the last element of the initial array y) and not a vector. After that, SSE is computed by subtracting a scalar from a vector:
np.sum((pred_happiness-y)**2. After changing the iterating variable name SSE is computed correctly, so the original y vector is subtracted from the pred_happiness vector.

On page 91 you enumerate matrix spaces, mentioning that the fourth one is right null space, but in the Resume on page 106 you again enumerate them, but this time mentioning left-null space. Which one is correct?
Where can I find errata?

Hello

Noticed that you wrote two textbooks about linear algebra:
i. Linear Algebra: Theory, Intuition, Code
ii. Practical Linear Algebra for Data Science

Based on their descriptions, I would assume that book i. has more content than book ii. and that everything that is book ii. is also in book i.
Is this correct?

With kind regards
Tim

Page 232 shows the incorrect formula: $C = A B^{-1}$. From the previous formula $Av = λBv$ we can derive $C = B^{-1}A$, instead of $C = A B^{-1}$ this way:
$Av = λBv$, $B^{-1}Av = B^{-1}λBv$, $(B^{-1}A) v = λ (B^{-1}B) v$, $Cv = λIv = λv$
So $C = B^{-1}A$

Also, I tested this in the notebook for Chapter 13 by adding some code in the section "Generalized eigendecomposition":
...
C1 = np.linalg.inv(B) @ A
C2 = A @ np.linalg.inv(B)
print(np.round(C1 @ evecs - evals * evecs,6))
print(np.round(C2 @ evecs - evals * evecs,6))
Output:

[[-0. -0. -0.  0.]
 [-0.  0.  0.  0.]
 [ 0.  0.  0.  0.]
 [-0. -0.  0.  0.]]
[[ 0.595699  0.643987  0.379455  0.922702]
 [ 0.704559  0.913965  0.558771 -4.758518]
 [-0.578492 -0.805236 -0.496454  5.629797]
 [ 1.53264   1.720669  1.008171 -0.076947]]