mikexcohen / linalgbook

Python and MATLAB code for linear algebra textbook.

LinAlgBook

This is all the code that accompanies the book "Linear Algebra: Theory, Intuition, Code"

https://www.amazon.com/Linear-Algebra-Theory-Intuition-Code/dp/9083136604

Note: For an independent translation of the book code into R, see the following link: https://alexander-pastukhov.github.io/cohen-linear-algebra/

And for an indepenedent translation into C++, see: https://github.com/thehoglet/LinAlgBook

linalgbook's Issues

Error on Chapter 6 practice problems, page 169

Hi Mike, thanks for creating this fantastic book. I've tried many different linear algebra text books by various authors (Gilbert Strang included) but this one was the only one that gave me that "a-ha" moment.

Anyways, thought I'd like to point out that the error on page 169, practice problem a where it asks to calculate the Euclidean distance between the following pairs of matrices.
The answer in the book is sqrt(322) but I think the correct answer should be sqrt(306).

C++ Version of Exercises

Repo is here:

LinAlgBook

Mostly based on your MATLAB solutions.

Great book! Thanks.

Practice Problem 2.4 (p.g. 34)

Hi there

Enjoying the book so far!

I believe b) should equal a column vector as [0 1 100] not [0 1 -20], as 0 - (-60) + (40) = 100

Ta
MH

Answers for Ex 3.10 question 2

Hi Mike

Not sure if this is the best place but I can't seem to find the answers showing the proofs for Exercises 3.10 Q2.

Struggling to unwind some of these equations to prove equality. Been battling with 2b for sometime now. And I'm sure I'm going to hit some walls down the track too...

If they are not available I will post on mathoverflow or something...

Many thanks in advance!

MH

Typo in equation 17.6, section 17.1 page 517

In the formula on page 517, when v.T@A@v is expanded.
We get (ax+cy)x + (bx+dy)y but then the following we end up with ax^2 + (c+d)xy + dy^2.
I think this should be ax^2 + (b+c)xy + dy^2

typo in Chapter 8.6 on page 217 and page 218

At the top of page 217 in the 2nd example, the vector of four 1's should be a vector of 5 1's.
The "A" vector is 2 x 5, so the "Y" vector needs to be 5 x 1

For the same "A" matrix as above, on page 218 (8.17) the right hand side is a row of 4 zeros.
I think it should be a row of 5 zeros.

Question about Figure 8.1 on page 211

Should C(M) be C(A) in the text for Figure 8.1 on page 211?

Possible typo on page 431

On page 431, in the paragraph on "Diagonalization", the book says Equation 15.21 is derived from Equation 15.19 by a left multiplication of V inverse. I think it is a right multiplication.

Possible typo on Page 365, Chapter 13.3

Thanks again for this amazing book.

The first sentence of the last paragraph on Page 365 says:
"The idea is that we want to break up "w" into two separate vectors, one of which is para;;el to "w" and the other is
perpendicular to "w".
I think the last 2 "w"'s should be the vector v.

On Page 358, there is a note (to the left of the figure) that the letter b is being overloaded to represent the point b and the vector "b", so the following comment might not be pertinent.
For pages 358-361 sometimes the vector "b" is written as a just a lower case b and sometimes as a bold lower case b.

On Page 375, row 2, column 2 of Q looks like it was not copied correctly for vector v2*
v2* = sqrt(5) / (10 * sqrt(2)) * (6 -2)' in the book.
The first element is sqrt(5) / (10 * sqrt(2)) * 6, which is 3/5 * (sqrt(5) / sqrt(2)), so row 1, column 2 of Q looks ok
The second element is sqrt(5) / (10 * sqrt(2)) * -2, which is -1/5 * (sqrt(5) / sqrt(2)), which should be put in row 2, column 2 of Q instead of 3 / 10 * (sqrt(5) / sqrt(2))

As a check, the length of the column 2 vector in the original Q is 54/ 50. For the new Q the length of the column 2 vector is 1.
Also, for column 1 and column 2 to be orthogonal, one of the 4 numbers must be negative.
Using the new Q, the dot product of column 1 and the new column 2 is 0.

As an interesting note, v2* is calculated using v1, not v1*.
But v3* looks like it is calculated using v1* and v2*
I thought this might mean v2* was wrong, but it looks like the normalizing factor 1 / sqrt(10) for v1 cancels out in the v2* equation.

Typos in Chapter 15

Amazing book!!!

On pages 417 and 418, I see 4 references to Figure 15.3, I think they should be references to Figure 15,2

On page 430, I think the diagonal entries (when lamda2 = -1) for A - lamda2 * I are wrong.
The diagonal entries for A are 1, 3, 6, and since lamda2 is -1, the entries should be:
1 - (-1) = 2, 3 - (-1)= 4, 6 - (-1) = 7, not 1 - 1, 3 - 1, 6 - 1

Possible typo in Chapter 8.2 on Page 209

I think the last line on page 209 has a typo.
"If the column space of AA(T) is a subset of the column space of AA(T) and those two subspaces have the same dimensionality, then they must be equal."

I think the second "AA(T)" should just be "A".

Awesome book, you provide great insight.