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Time management is very much important in IIT JAM. The eduncle test series for IIT JAM Mathematical Statistics helped me a lot in this portion. I am very thankful to the test series I bought from eduncle.
Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
- IIT JAM
- Mathematics (MA)
Please send the solution to the problem given in the attachment.
please send the solution to the problem given in the attachment.
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Deepak singh 1 Best Answer
The minimal polynomial M(x) of an n × n matrix A over a field F is the monic polynomial P over F(field ) of least degree such that P(A) = 0. Any other polynomial Q with Q(A) = 0 is a multiple of M(x).
I couldn't understand clearly.
Refer attached example.
what is the difference between char. poly. and minimal poly.?
degree of characteristics polynomial of matrix n×n is always n . But degree of minimal polynomial will be less than or equal to n . And minimal polynomial always divides characteristics polynomial but characteristics polynomial divides minimal only when degree of minimal is n.
similarities is that both polynomial satisfies matrix . And both contains same factors of form (x-a) where a is eigenvalue without multiplicity.