What is Homodromy in Linear Algebra?
In the context of linear algebra, a matrix is said to be homodromous if its eigenvalues all have the same absolute value. In other words, if all the eigenvalues of a matrix have the same magnitude but different signs, then the matrix is homodromous.
For example, consider the following matrix:
[1 0]
[0 1]
The eigenvalues of this matrix are 1 and -1, and both have the same absolute value (1), so this matrix is homodromous.
On the other hand, the following matrix is not homodromous:
[2 1]
[1 2]
The eigenvalues of this matrix are 2 and 1, but they do not all have the same absolute value (2 and 1 have different absolute values), so this matrix is not homodromous.
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