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Singular value
Square roots of the eigenvalues of the self-adjoint operator
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Jacobian Spectra (1) Β· Gradient-based Training (1) Β· Deep Neural Networks (1) Β· Implicit Bias (1) Β· Singular Values (1) Β· Spectral Separation (1) Β· arXiv (1)
π Key Information
In mathematics, in particular functional analysis, the singular values of a compact operator
T
:
X
β
Y
{\displaystyle T:X\rightarrow Y}
acting between Hilbert spaces
X
{\displaystyle X}
and
Y
{\displaystyle Y}
, are the square roots of the (necessarily non-negative) eigenvalues of the self-adjoint operator
T
β
T
{\displaystyle T^{*}T}
(where
T
β
{\displaystyle T^{*}}
denotes the adjoint of
T
{\displaystyle T}
).
The singular values are non-negative real numbers, usually listed in decreasing order (Ο1(T), Ο2(T), β¦). The largest singular value Ο1(T) is equal to the operator norm of T (see Min-max theorem).
π° Related News (1)
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