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Orthogonality In Normed Spaces, Martin R. Mccarthy

All Master's Theses

This paper presents three definitions of orthogonality in normed spaces. Each definition is shown equivalent to the inner product being zero when restricted to an inner product space. The definitions arise from such properties in two space as the diagonals of a rectangle being equal and the Pythagorean Theorem. The third definition shows that the idea of an inner product can be generalized under certain conditions.