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uare ma momial (2) of least degree such that $(1) = 0. position: Two important facts regarding the eigenvalues of a matrix, A E Cnxn (A may have ,complex, distinct or repeted igenvalues): det(A) = I[Ai Trace(A) = > %3D i=1

uare ma momial (2) of least degree such that $(1) = 0. position: Two important facts regarding the eigenvalues of a matrix, A E Cnxn (A may have ,complex, distinct or repeted igenvalues): det(A) = I[Ai Trace(A) = > %3D i=1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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can you please show the proof of this theorem?

Definition(Minimal Polynomial): Minimal polynomial of square matrix A is the monic polynomial p(1) of least degree such that (1) = 0. Proposition: Two important facts regarding the eigenvalues of a matrix, A E cnxn (A may have real, complex, distinct or repeted igenvalues): det(A) = ||Ai i=1 Trace(A) = di i=1
Transcribed Image Text:Definition(Minimal Polynomial): Minimal polynomial of square matrix A is the monic polynomial p(1) of least degree such that (1) = 0. Proposition: Two important facts regarding the eigenvalues of a matrix, A E cnxn (A may have real, complex, distinct or repeted igenvalues): det(A) = ||Ai i=1 Trace(A) = di i=1
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