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My name is Jestine (34 years old) and my hobbies are Origami and Microscopy.

Here is my web site; http://Www.hostgator1centcoupon.info/ (support.file1.com) In matrix theory, the spread of a matrix describes how far apart the eigenvalues are in the complex plane.

Suppose $A$ is a square matrix with eigenvalues ${\lambda }_1,\dots ,{\lambda }_n$. Then the spread of $A$ is the non-negative number

$s(A)=\max \{|{\lambda }_i-{\lambda }_j|:i,j=1,\dots n\}.$

Examples

• For the zero matrix and the identity matrix, the spread is zero.
• Only $0$ and $1$ can be eigenvalues for a projection. A projection matrix therefore has spread $0$ or $1$.
• All eigenvalues of an unitary matrix $A$ lie on the unit circle. Hence $s(A)\le 2$.
• The spread of a matrix depends only on the spectrum of the matrix, so if $B$ is invertible, then

$s(A)=s(BA{B}^{-1}).$

See also

• Field of values

References

• Marvin Marcus and Henryk Minc, A survey of matrix theory and matrix inequalities, Dover Publications, 1992, ISBN 0-486-67102-X. Chap.III.4.

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