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Get the Eigenvalues of a particular Matrix?

Posted 4 years ago

Hi, How do we get the Eigenvalues of a particular Matrix?

matrix = {{1, 0, 7, 0}, {0, 1, 2, 0}, {1, 1, 2, (4 - 1)}, {0, 1, a, 
    3}};
matrix // MatrixForm
eig = Eigenvalues[matrix];
N[eig]

This is a simple example, and I have a more complex symbolic matrix. However, i am not able to get 4 eigenvalues for this simple matrix above.

My output looks like this

{1, Root[15 + 3 a + (2 - 3 a) #1 - 6 #1^2 + #1^3 &, 1], 
 Root[15 + 3 a + (2 - 3 a) #1 - 6 #1^2 + #1^3 &, 2], 
 Root[15 + 3 a + (2 - 3 a) #1 - 6 #1^2 + #1^3 &, 3]}

I do not understand the #1 terms. Any help is appreciated. Thank you all.

POSTED BY: Sattik Basu
4 Replies

I count four eigenvalues there.

POSTED BY: Daniel Lichtblau
Posted 4 years ago

Hi Daniel, yes, there are 4 expressions in the output. However, I could not understand the terms that had "#1" at the end. However, using ToRadicals[..], it cleared out the mess.

POSTED BY: Sattik Basu
Posted 4 years ago

Try

ToRadicals[eig]
POSTED BY: Bill Nelson
Posted 4 years ago

Thanks, that worked like a charm.

POSTED BY: Sattik Basu
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