Describe the mistake
p. 127 states: "The nonzero singular values of A are the square roots of the nonzero eigenvalues of A A^T and are equal to the nonzero eigenvalues of A^T A."
But: above it says that the singular values are the square roots of both the eigenvalues of A^T A (p.123 Eq. 4.75) and of the eigenvalues of A A^T (p. 124 below Eq. 4.78).
Location
version 2020-09-12
Chapter 4
page 127
last second-level bullet point
Proposed solution
Rewrite the bullet point in the summary on p. 127: "The nonzero singular values of A are the square roots of the nonzero eigenvalues of both A A^T and A^T A." (or a better formulation)
mpd37
commented
3 years ago
Describe the mistake p. 127 states: "The nonzero singular values of A are the square roots of the nonzero eigenvalues of A A^T and are equal to the nonzero eigenvalues of A^T A."
But: above it says that the singular values are the square roots of both the eigenvalues of A^T A (p.123 Eq. 4.75) and of the eigenvalues of A A^T (p. 124 below Eq. 4.78).
Location
Proposed solution Rewrite the bullet point in the summary on p. 127: "The nonzero singular values of A are the square roots of the nonzero eigenvalues of both A A^T and A^T A." (or a better formulation)
Notes Confirmed via Wikipedia.