Jordan Forms, Nullity and Minimal Polynomials

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Homework Statement


Nullity(B-5I)=2 and Nullity(B-5I)^2=5
Characteristic poly is: (λ-5)^12
Find the possible jordan forms of B and the minimal polynomials for each of these JFs.

The Attempt at a Solution


JFs: Jn1(5) or ... or Jni(5).
Not sure how to find these jordan forms and minimal polynomials.
 
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shaon0 said:

Homework Statement


Nullity(B-5I)=2 and Nullity(B-5I)^2=5
Characteristic poly is: (λ-5)^12
Find the possible jordan forms of B and the minimal polynomials for each of these JFs.

The Attempt at a Solution


JFs: Jn1(5) or ... or Jni(5).
Not sure how to find these jordan forms and minimal polynomials.

Bump
 
What does "minimal polynomial" for a matrix mean? What do you know about the relation between the minimal polynomial of a matrix and its eigenvectors?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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