The essential ingredient for the study of square matrices is the determinant. For reasons given in Section 3.5, as well as in Chapter 9, it is useful to consider matrices with entries in a ring. This allows us to consider matrices with entries in(rational integers) as well as in K[X] (polynomials with coefficients in K).We assume that the ring of scalars A is a commutative (meaning that the multiplication is commutative) integral domain (meaning that it does not have divisors of zero: ab=0 implies either a = 0 or b = 0), with a unit denoted by 1, that is, an element satisfying 1x = x1 = x for every x ∈≤ A.
KeywordsCharacteristic Polynomial Integral Domain Triangular Matrix Minimal Polynomial Simple Eigenvalue
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