| Summary: | 碩士 === 東吳大學 === 數學系 === 95 === Let A be a n-by-n complex matrix; the numerical range of A is defined to be the set {x*Ax:x belongs to C^n,x*x=1}. The image of W(A^k) where k is a positive integer is studied. In particular, the geometric properties of W(A^k) related to that of W(A) are examined.
Section 1 introduces several important elementary properties of W(A).
Section 2 examines the numerical range of powers of normal matrices, unitary matrices, hermitian matrices, skew-hermitian matrices.
Section 3 describes the numerical range of powers of 2-by-2 matrices.
Section 4 studies the numerical range of powers of 3-by-3 matrices.
Section 5 examines the numerical range of powers of 4-by-4 matrices.
Section 6 deals with the numerical range of powers of n-by-n matrices.
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