The discussion focuses on determining the Jordan forms and minimal polynomials for a matrix B given the nullities Nullity(B-5I)=2 and Nullity(B-5I)^2=5, with a characteristic polynomial of (λ-5)^12. The possible Jordan forms of B include Jn1(5) through Jni(5), where 'n' denotes the size of the Jordan blocks. The minimal polynomial is directly related to the structure of these Jordan forms, specifically reflecting the eigenvalue's algebraic and geometric multiplicities.
PREREQUISITESStudents and professionals in linear algebra, particularly those studying matrix theory, eigenvalue problems, and Jordan forms. This discussion is beneficial for anyone seeking to deepen their understanding of minimal polynomials and their applications in matrix analysis.
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.