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The classical Sherman-Morrison-Woodbury (for short SMW) formula A+YGZ*-1=A-1-A-1YG-1+Z*A-1Y-1Z*A-1 is generalized to the {2}-inverse case. Some sufficient conditions under which the SMW formula can be represented as A+YGZ*-=A--A-YG-+Z*A-Y-Z*A- are obtained

abstract and applied analysis

A Generalization of the SMW Formula of Operator<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:mi>Y</mml:mi><mml:mi>G</mml:mi><mml:msup><mml:mrow><mml:mi>Z</mml:mi></mml:mrow><mml:mrow><mml:mi>*</mml:mi></mml:mrow></mml:msup></mml:math>to the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mo stretchy="false">{</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">}</mml:mo></mml:math>-Inverse Case

A Generalization of the SMW Formula of OperatorA+YGZ*to the{2}-Inverse Case