- #1

pivoxa15

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1. If given a matrix in JNF, what would be its basis? How would you calculate it?

If you put the basis vectors (of JNF) as columns in matrix P than

P=(T^-1)PA, T and A are given.

where T is the original matrix and A is T in JNF. But I cannot explicitly calculate P since it is on both sides. How do I find P?

2. If the minimal polynomial is given as (x+2)(x-4)=0, and the -2 eigenvalue results in a 0 dimensional null space (i.e. (0,0,0) vector) what would the JNF look like given the null space of eigenvalue 4 is 2 dimensional. And the original matrix is 3 by 3.

Would it be

diag(0,4,4)?

If you put the basis vectors (of JNF) as columns in matrix P than

P=(T^-1)PA, T and A are given.

where T is the original matrix and A is T in JNF. But I cannot explicitly calculate P since it is on both sides. How do I find P?

2. If the minimal polynomial is given as (x+2)(x-4)=0, and the -2 eigenvalue results in a 0 dimensional null space (i.e. (0,0,0) vector) what would the JNF look like given the null space of eigenvalue 4 is 2 dimensional. And the original matrix is 3 by 3.

Would it be

diag(0,4,4)?

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