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Elementary Symmetric Polynomials and the Characteristic Polynomial
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We define the elementary symmetric polynomials. We show that when the characteristic equation of a square matrix is factored, the symmetric polynomials of the eigenvalues of the matrix are the coefficients of the original characteristic equation. This will give us a formula for the determinant and trace of the matrix in terms of the eigenvalues.
#mikethemathematician, #profdabkowski, #mikedabkowski
#mikethemathematician, #profdabkowski, #mikedabkowski
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