The Nullity, Rank, and Invertibility of Linear Combinations of k-Potent Matrices
نویسندگان
چکیده
منابع مشابه
INVERTIBILITY AND FREDHOLMNESS OF LINEAR COMBINATIONS OF QUADRATIC, k-POTENT AND NILPOTENT OPERATORS
Recently, the invertibility of linear combinations of two idempotents has been studied by several authors. Let P and Q be idempotents in a Banach algebra. It was shown that the invertibility of P + Q is equivalent to that of aP + bQ for nonzero a, b with a + b 6= 0. In this note, we obtain a similar result for square zero operators and those operators satisfying x = dx for some scalar d. More g...
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چکیده ندارد.
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In this article we present a proof of the result known in Linear Algebra as the “rank nullity Theorem”, which states that, given any linear form f from a finite dimensional vector space V to a vector space W , then the dimension of V is equal to the dimension of the kernel of f (which is a subspace of V ) and the dimension of the range of f (which is a subspace of W ). The proof presented here ...
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ژورنال
عنوان ژورنال: Mathematics
سال: 2020
ISSN: 2227-7390
DOI: 10.3390/math8122147