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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 , .
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For example, a bilinear form is the same thing as a (0, 2)-tensor; an inner product is an example of a (0, 2)-tensor, but not all (0, 2)-tensors are inner products. In the (0, M ) -entry of the table, M denotes the dimensionality of the underlying vector space or manifold because for each dimension of the space, a separate index is needed to ...
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 .
Tesla's stock price reached $420 on Wednesday afternoon, which elicited responses from social media users and the company's CEO, Elon Musk. "As foretold in the prophecy," Musk wrote in an X post ...
“It’s not a question of a price tag,” the president-elect told NBC News recently. “We have no choice. “We have no choice. They’re not staying here.”
An important affine connection in general relativity is the Levi-Civita connection, which is a symmetric connection obtained from parallel transporting a tangent vector along a curve whilst keeping the inner product of that vector constant along the curve.
A person was arrested after attempting to climb a temporary fence near the White House this morning, according to a U.S. Secret Service spokesperson. The Secret Service said the person was ...