Perron-Frobenius Theorem
If all elements 
of an Irreducible Matrix 
are Nonnegative, then 
is anEigenvalue of and all the Eigenvalues of lie on the Disk
where, if
is a set of Nonnegative numbers (which are not allzero),
and
. Furthermore, if has exactly 
Eigenvalues 
on theCircle 
, then the set of all its Eigenvalues is invariant under rotations by
about the Origin.See also Wielandt's Theorem
References
Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, p. 1121, 1979.
- Brocard Triangles
- Bromwich Integral
- Brothers
- Brouwer Fixed Point Theorem
- Browkin's Theorem
- Brown Function
- Brown Numbers
- Brown's Criterion
- Broyden's Method
- Bruck-Ryser-Chowla Theorem
- Bruck-Ryser Theorem
- Brunnian Link
- Brunn-Minkowski Inequality
- Brun's Constant
- Brun's Sum
- Brun's Theorem
- Brute Force Factorization
- B-Spline
- B-Tree
- Bubble
- Buchberger's Algorithm
- Buckminster Fuller Dome
- Buffon-Laplace Needle Problem
- Buffon's Needle Problem
- Bulirsch-Stoer Algorithm