Matrix type

Matrix eigenvalues

${\lambda }_j,j=1,\cdots ,n$

Harmonic

${\lambda }_j=1/j$

Harmonic roots

${\lambda }_j={\left(1/j\right)}^{1/2}$

Geometric decay

${\lambda }_j={\left(0.95\right)}^j$

Moderate geometric decay

${\lambda }_j={\left(0.99\right)}^j$

Slow geometric decay

${\lambda }_j={\left(0.999\right)}^j$

Very slow geometric decay

${\lambda }_j={\left(0.9999\right)}^j$

Equispaced

${\lambda }_j=\left(1001-j\right)/1000$ for $j\mathrm{<mo>\; =\; </mo>1},\cdots ,1000$ ,

${\lambda }_j=1/j$ for $j=1001,\cdots ,n$

Densely equispaced

${\lambda }_j=\left(10001-j\right)/10000$ for $j=1,\cdots ,10000$ ,

${\lambda }_j=1/j$ for $j=10001,\cdots ,n$

Normal distribution

Normally distributed eigenvalues