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In mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space [1] [2]) is a real vector space or a complex vector space with an operation called an inner product. The inner product of two vectors in the space is a scalar, often denoted with angle brackets such as in , .
A real inner product space is defined in the same way, except that H is a real vector space and the inner product takes real values. Such an inner product will be a bilinear map and ( H , H , ⋅ , ⋅ ) {\displaystyle (H,H,\langle \cdot ,\cdot \rangle )} will form a dual system .
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John Paul holds a microphone for one of his daughters not long after he joined WSOC-TV Channel 9 in Charlotte, NC, in 2015. Paul announced on July 25, 2022, that he will be leaving the station for ...
WNCT-TV (channel 9) is a television station licensed to Greenville, North Carolina, United States, serving Eastern North Carolina as an affiliate of CBS. Its second digital subchannel serves as an owned-and-operated station of The CW (via The CW Plus ).
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This article will deal with the second, called a L-semi-inner product or semi-inner product in the sense of Lumer, which is an inner product not required to be conjugate symmetric. It was formulated by Günter Lumer , for the purpose of extending Hilbert space type arguments to Banach spaces in functional analysis . [ 1 ]