properties of singular values of a complex matrix
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Suppose $G$ is a complex $ntimes n$ matrix Could anyone help me to prove the following where $sigma$'s are singular values of $G$?
$det Gne 0 Leftrightarrow sigma_{min}[G]>0$.
$sigma_{max}[G^{-1}]=frac{1}{sigma_{min}[G]}$ if $sigma_{min}[G]>0$
$sigma_{min}[I+G]ge 1-sigma_{max}[G]$
$sigma_{max}[G_1G_2]le sigma_{max}[G_1]sigma_{max}[G_2]$ for complex matrices $G_1,G_2$
singularvalues
asked Nov 21 at 17:09
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up vote
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Suppose $G$ is a complex $ntimes n$ matrix Could anyone help me to prove the following where $sigma$'s are singular values of $G$?
$det Gne 0 Leftrightarrow sigma_{min}[G]>0$.
$sigma_{max}[G^{-1}]=frac{1}{sigma_{min}[G]}$ if $sigma_{min}[G]>0$
$sigma_{min}[I+G]ge 1-sigma_{max}[G]$
$sigma_{max}[G_1G_2]le sigma_{max}[G_1]sigma_{max}[G_2]$ for complex matrices $G_1,G_2$
singularvalues
asked Nov 21 at 17:09
Wow
17k955174
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Suppose $G$ is a complex $ntimes n$ matrix Could anyone help me to prove the following where $sigma$'s are singular values of $G$?
$det Gne 0 Leftrightarrow sigma_{min}[G]>0$.
$sigma_{max}[G^{-1}]=frac{1}{sigma_{min}[G]}$ if $sigma_{min}[G]>0$
$sigma_{min}[I+G]ge 1-sigma_{max}[G]$
$sigma_{max}[G_1G_2]le sigma_{max}[G_1]sigma_{max}[G_2]$ for complex matrices $G_1,G_2$
singularvalues
asked Nov 21 at 17:09
Wow
17k955174
Suppose $G$ is a complex $ntimes n$ matrix Could anyone help me to prove the following where $sigma$'s are singular values of $G$?
$det Gne 0 Leftrightarrow sigma_{min}[G]>0$.
$sigma_{max}[G^{-1}]=frac{1}{sigma_{min}[G]}$ if $sigma_{min}[G]>0$
$sigma_{min}[I+G]ge 1-sigma_{max}[G]$
$sigma_{max}[G_1G_2]le sigma_{max}[G_1]sigma_{max}[G_2]$ for complex matrices $G_1,G_2$
singularvalues
singularvalues
asked Nov 21 at 17:09
Wow
17k955174
asked Nov 21 at 17:09
Wow
17k955174
asked Nov 21 at 17:09
Wow
17k955174
asked Nov 21 at 17:09
Wow
17k955174
asked Nov 21 at 17:09
Wow
17k955174
17k955174
add a comment |
add a comment |
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