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.
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.