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An Introduction to the Theory of Determinants,In this chapter, we will introduce and study a remarkable function called the determinant, which assigns to an . matrix . over a field . a scalar . having two remarkable properties: . if and only if . is invertible, and if . is also in ., then .. The latter property is referred to as the product formula.

诱导

Vector Spaces,A vector space is a set . whose elements, called vectors, can be added and subtracted: in fact, a vector space is an abelian group under addition.

坦白

Linear Mappings,The purpose of this chapter is to introduce linear mappings.

myopia

exhilaration

埋葬

filial

Conference proceedings 20091st edition. and its minimal polynomial has only simple roots. It would be useful to have a result that would allow one to predict that . is semisimple on the basis of a criterion that is simpler than finding the minimal polynomial, which, after all, requires knowing the roots of the characteristic polynomial.

characteristic

Some Promising Trends in Ice Mechanics,rary linear mapping . having the property that all the roots of its characteristic polynomial lie in .. To describe this situation, let us say that . contains the eigenvalues of .. Recall that a linear mapping . is also called an endomorphism of ., and in this chapter, we will usually use that term.

MAOIS

Unitary Diagonalization and Quadratic Forms,. and its minimal polynomial has only simple roots. It would be useful to have a result that would allow one to predict that . is semisimple on the basis of a criterion that is simpler than finding the minimal polynomial, which, after all, requires knowing the roots of the characteristic polynomial.

珐琅

The Structure Theory of Linear Mappings,rary linear mapping . having the property that all the roots of its characteristic polynomial lie in .. To describe this situation, let us say that . contains the eigenvalues of .. Recall that a linear mapping . is also called an endomorphism of ., and in this chapter, we will usually use that term.