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I have a symmetric matrix as shown below

$$\begin{pmatrix} 0&2&1&4&3 \\ 2&0&1&2&1 \\ 1&1&0&3&2 \\4&2&3&0&1 \\ 3&1&2&1&0\end{pmatrix}$$

Does this matrix belong to a particular type?

I am CS student and not familiar with types of matrices. I am researching to know the particular matrix type since I have a huge collection of matrices similar to this one. By knowing the type of matrix, maybe I can go through its properties and work around easier ways to process data efficiently. I am working on a research project in Data Mining. Please help.

P.S.: Only the diagonal elements are zero. Non diagonal elements are positive.

Rodrigo de Azevedo
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Shankar
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    See: http://math.stackexchange.com/questions/79779/properties-of-zero-diagonal-symmetric-matrices, http://math.stackexchange.com/questions/144148/determinant-of-symmetric-matrix-with-the-main-diagonal-elements-zero to start, perhaps. – Ian Coley Apr 22 '13 at 21:30
  • This matrix cannot be pozitive/negative definite. Because $e_i^TAe_i = 0 $. – tom Apr 22 '13 at 21:31

1 Answers1

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This is a hollow matrix. You can say that the sum of its eigenvalues equals zero.

bersou
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