- #1

joypav

- 151

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I have to show that the matrix 10x10 matrix below is nilpotent, determine its signature, and find its Jordan canonical form.

[-2 , 19/2 , -17/2 , 0 , -13 , 9 , -4 , 7 , -2 , -13]

[15 , -51 , 48 , -8 , 80 , -48 , 19 , -39 , 10 , 74]

[-7 , 34 , -33 , 0 , -50 , 31 , -11 , 27 , -6 , -47]

[1 , -4 , 4 , -1 , 7 , -4 , 1 , -3 , 1 , 6]

[0 , -2 , 2 , 0 , 3 , -2 , 1 , -1 , 0 , 3]

[-11 , 91/2 , -87/2 , 4 , -70 , 42 , -16 , 35 , -8 , -65]

[-1 , 9/2 , -9/2 , 0 , -7 , 4 , -1 , 4 , -1 , -6]

[-9 , 39 , -37 , 2 , -58 , 36 , -14 , 30 , -7 , -55]

[-7 , 32 , -31 , 1 , -48 , 29 , -11 , 25 , -5 , -45]

[5 , -25/2 , 23/2 , -3 , 20 , -12 , 5 , -10 , 3 , 18]

I've shown that the matrix to the sixth power is the zero matrix (so it's nilpotent). And I believe the signature is (0, 5, 0, 3, 0, 2).. if I've done it correctly.

Anyways, I have not yet found the Jordan Canonical form. We are allowed to use Maple but I do not yet have it for my laptop (an old professor of mine said he would get it for me so I don't have to pay). I know there is a command in Maple that will find it for you.

Could someone with Maple (or Matlab) find it for me? I would really appreciate it!