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August 12

Polynomial determinants

What exactly are they used for? 70.112.97.77 (talk) 14:14, 12 August 2013 (UTC)[reply]

Not sure if this is what you're asking about, but to find the eigenvalues of a matrix you add minus lambda times the identity matrix to the matrix in question, then take the determinant of the resulting matrix, which gives a polynomial in lambda. The zeroes of this polynomial are the eigenvalues of the original matrix. This has applications in, for example, solving matrix difference equations. For example, such an equation is stable (the state variables converge over time) if and only if all the eigenvalues are less than 1 in magnitude. Duoduoduo (talk) 17:10, 12 August 2013 (UTC)[reply]

See also Matrix differential equation, in which stability obtains if and only if all the eigenvalues are negative. Duoduoduo (talk) 17:40, 12 August 2013 (UTC)[reply]