Numerical Shadow

The web resource on numerical range and numerical shadow

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numerical-shadow:examples:2x2

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numerical-shadow:examples:2x2 [2013/04/16 00:23]
lpawela specialcases:2x2 renamed to numerical-shadow:examples:2x2
numerical-shadow:examples:2x2 [2018/05/22 14:21] (current)
plewandowska
Line 11: Line 11:
 <​html></​center></​html>​ <​html></​center></​html>​
  
 +====== Non-normal matrices ======
  
 +==== Example 1 ====
 +
 +The matrix is $$\begin{pmatrix}
 +0&1\\
 +0&0
 +\end{pmatrix}.$$ The shadow resembles a physical shadow cast by the hollow sphere made of transparent material when illuminated by a light source at infinity.
 +
 +
 +<​html><​center></​html>​
 +^  Standard numerical shadow with respect to complex states. ​ ^   ​Cross-section of the shadow along the real axis.  ^
 +|  {{:​numerical-shadow:​examples:​sec2fig1a.png?​nolink&​300|Standard numerical shadow with respect to complex states}} ​ |  {{:​numerical-shadow:​examples:​sec2fig1b.png?​nolink&​300|Numerical shadow with respect to real states}} ​ |
 +<​html></​center></​html>​
 +
 +==== Example 2 ====
 +
 +The matrix is $$\begin{pmatrix}
 +0&1\\
 +0&1
 +\end{pmatrix}.$$ The shadow resembles physical shadow cast by the hollow sphere made of transparent material when illuminated by a light source at infinity, but with screen not perpendicular to the light rays.
 +
 +<​html><​center></​html>​
 +^  Standard numerical shadow with respect to complex states. ​ ^   ​Cross-section of the shadow along the real axis.  ^
 +|  {{:​numerical-shadow:​examples:​sec2fig1c.png?​nolink&​300|Standard numerical shadow with respect to complex states}} ​ |  {{:​numerical-shadow:​examples:​sec2fig1d.png?​nolink&​300|Numerical shadow with respect to real states}} ​ |
 +<​html></​center></​html>​
numerical-shadow/examples/2x2.1366071834.txt.gz · Last modified: 2013/04/16 00:23 by lpawela