Comments (2)
Thank you for your suggestion; your argument totally makes sense.
However, I would suggest a different correction; see my comments below.
I suppose that, throughout the concerned section ``Eigenvector Equation'' beginning at page 698, A is assumed to be square (because eigen things make sense only for squre matrices), and, from the second paragraph at page 699, A is also assumed to be symmetric (although (C.47) and (C.48) hold for non-symmetric matrices as well).
So, it feels more consistent to me to correct as follows:
Page 701
Paragraph 2, Line 1: A matrix $\mathbf{A}$'' should read
A symmetric matrix
As you might have already noticed, a drawback of the above correction is that we should also correct (C.49):
Page 701
Equation (C.49) and the following line: To be consistent with our definition of positive definitness of a square matrix, we should give a symmetric matrix as an example of a non-definite matrix such that all the elements are positive. For instance, a symmetric matrix of the form
\begin{pmatrix}
1 & 2
2 & 1
\end{pmatrix}
has eigenvalues -1 and 3.
It might be helpful to also give an example of a positive-definite matrix such that some (non-diagonal) elements are negative, e.g.,
\begin{pmatrix}
1 & -2
-2 & 5
\end{pmatrix}
has positive eigenvalues.
from prml_errata.
I think that your comment is clear and consistent and can agree with you.
Thank you for you efforts to make PRML more clear. Your errata document is invaluable source to study PRML.
from prml_errata.
Related Issues (18)
- Self-contained proof for Wishart distribution
- Introduce paragraphs and paragraph headers
- Add some more properties of log minus digamma function
- Expand on robust regression
- Give some motivation for Fisher information matrix
- Add errata for some hyphenation inconsistencies HOT 1
- Kronecker's delta used w/o definition
- Success probability $\mu$ for Bernoulli should be restricted on $(0, 1)$
- Dismissal of "bayesian methods don't overfit" is too quick HOT 11
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- Link to official support page broken
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- Error in eq. (3.99) HOT 2
- I believe M should be 4 in 5.5. Regularization in Neural Networks, p256
- Errata fixed by Bishop is correct at page 101? HOT 2
- Errata in Figure 10.2 HOT 3
- Errata at page 35 in More PRML Errata
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from prml_errata.