Projections, generalized inverses, and quadratic forms
نویسندگان
چکیده
منابع مشابه
Applications of quadratic D-forms to generalized quadratic forms
In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.
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In this article we characterize operators on Banach spaces which have the same projections related to their outer or inner generalized inverses. As corollaries, we obatin well-known results for the Drazin inverse of bounded operators.
متن کاملSpecial forms of generalized inverses of row block matrices
Given a row block matrix [A, B ], this paper investigates the relations between the generalized inverse [A, B ]− and the column block matrix [ A− B− ] consisting of two generalized inverses A− and B−. The first step of the investigation is to establish a formula for the minimal rank of the difference [A, B ]− − [ A− B− ] , the second step is to find a necessary and sufficient condition for [A, ...
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Given a row block matrix [A, B ], this paper investigates the relations between the generalized inverse [A, B ]− and the column block matrix [ A− B− ] consisting of two generalized inverses A− and B−. The first step of the investigation is to establish a formula for the minimal rank of the difference [A, B ]− − [ A− B− ] , the second step is to find a necessary and sufficient condition for [A, ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1964
ISSN: 0022-247X
DOI: 10.1016/0022-247x(64)90002-2