Numerical Shadow

The web resource on numerical range and numerical shadow

User Tools

Site Tools


numerical-shadow:examples:2x2

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision
Previous revision
numerical-shadow:examples:2x2 [2013/03/13 12:31]
lpawela
numerical-shadow:examples:2x2 [2018/05/22 14:21] (current)
plewandowska
Line 1: Line 1:
 +~~NOTOC~~
 ====== Hermitian matrices ====== ====== Hermitian matrices ======
 In the case of Hermitian matrices the numerical shadow is a one dimensional distribution. In the case of Hermitian matrices the numerical shadow is a one dimensional distribution.
Line 6: Line 7:
  
 <​html><​center></​html>​ <​html><​center></​html>​
-^  Standard numerical shadow with respect to complex states. ​ ^ +^  Standard numerical shadow with respect to complex ​states. ​ ^  Numerical shadow with respect to real states. ​ ^ 
-|  {{:​specialcases:​complex_a1.png?​nolink|Standard numerical shadow with respect to complex states}} ​ |+|  {{:​specialcases:​complex_a1.png?​nolink&300|Standard numerical shadow with respect to complex ​states}} ​ |  {{:​specialcases:​real_a1.png?​nolink&​300|Numerical shadow with respect to real states}} ​ |
 <​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>​ <​html><​center></​html>​
-^  Standard numerical shadow with respect to real states. ​ ^ +^  Standard numerical shadow with respect to complex ​states.  ^   ​Cross-section of the shadow along the real axis.  ^ 
-|  {{:specialcases:real_a1.png?​nolink|Numerical shadow with respect to real states}} ​ |+|  {{: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>​ <​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/2x2.1363177881.txt.gz · Last modified: 2013/03/13 12:31 by lpawela