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・ Tensor derivative (continuum mechanics)
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・ Tensor product of algebras
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Tensor product of quadratic forms
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Tensor product of quadratic forms : ウィキペディア英語版
Tensor product of quadratic forms

The tensor product of quadratic forms is most easily understood when one views the quadratic forms as ''quadratic spaces''. So, if (''V'', ''q''1) and (''W'', ''q''2) are quadratic spaces, with ''V'',''W'' vector spaces, then the tensor product is a quadratic form ''q'' on the tensor product of vector spaces ''V'' ⊗ ''W''.
It is defined in such a way that for v \otimes w \in V \otimes W we have q(v \otimes w) = q_1(v)q_2(w). In particular, if we have diagonalizations of our quadratic forms (which is always possible when the characteristic is not 2) such that
:q_1 \cong \langle a_1, ... , a_n \rangle
:q_2 \cong \langle b_1, ... , b_m \rangle
then the tensor product has diagonalization
:q_1 \otimes q_2 = q \cong \langle a_1b_1, a_1b_2, ... a_1b_m, a_2b_1, ... , a_2b_m , ... , a_nb_1, ... a_nb_m \rangle.


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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