Contraction (Tensor)
The contraction of a Tensor is obtained by setting unlike indices equal and summing according to theEinstein Summation convention. Contraction reduces the Rank of a Tensor by 2. For a second Rank Tensor,
Therefore, the contraction is invariant, and must be a Scalar. In fact, this Scalar is known as the Trace of a Matrix in Matrix theory.
References
Arfken, G. ``Contraction, Direct Product.'' §3.2 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 124-126, 1985.
- Bohr-Favard Inequalities
- Bolyai-Gerwein Theorem
- Bolzano Theorem
- Bolzano-Weierstraß Theorem
- Bolza Problem
- Bombieri Inner Product
- Bombieri Norm
- Bombieri's Inequality
- Bombieri's Theorem
- Bond Percolation
- Bonferroni Correction
- Bonferroni's Inequality
- Bonferroni Test
- Bonne Projection
- Book Stacking Problem
- Boolean Algebra
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- Boolean Function
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- Boole's Inequality
- Borchardt-Pfaff Algorithm
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- Bordism Group
- Borel-Cantelli Lemma