characteristic polynomial

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English[edit]

Noun[edit]

characteristic polynomial (plural characteristic polynomials)

  1. (linear algebra) The determinant, of a matrix minus an indeterminant times the identity matrix
    The characteristic polynomial of \left(\begin{array}{cc}1 & 4\\3 & -5\end{array}\right) is \mathbf{Det}\left(\begin{array}{cc}1-x & 4\\ 3 & -5-x\end{array}\right).

Usage notes[edit]

Equally many authors instead subtract the matrix from the indeterminant times the identity matrix. But the result only differs by multiplication by -1, which isn't important where characteristic polynomials are studied.

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