<![CDATA[In this paper, will be discussed about the minimum norm in the pre- Hilbert Space, Hilbert space and its modification, and its application. The results are: Let X be a pre-Hilbert space and M is a sub space of X. If an element is fixed, then : . If there is such that , then is unique. Let H be a Hilbert space and M be a closed sub space of H . If , then there is a unique element such that , . Let X be a Hilbert space , M be a closed sub space of X . If V =x+ M, for an element xX, then there is a unique element of such that , M.Key words : minimum norm, pre-Hilbert space, Hilbert space , orthogonality]]>
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