DYADS - Dyad A is formed by two vectors a and b (complex in...

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Dyad A is formed by two vectors a and b ( complex in general). Here, upper-case bold variables denote dyads (as well as general dyadics) whereas lower-case bold variables denote vectors. In matrix notation : In general algebraic form: where and are unit vectors (also known as coordinate axes) and i , j goes from 1 to the space dimension. A dyadic polynomial A , otherwise known as a dyadic, is formed from multiple vectors A dyadic which cannot be reduced to a sum of less than 3 dyads is said to be complete. In this case, the forming vectors are non-coplanar, see Chen (1983) . The following table classifies dyadics: Determinant Adjoint Matrix and its rank Zero = 0 = 0 = 0; rank 0: all zeroes Linear = 0 = 0 ≠ 0; rank 1: at least one non-zero element and all 2x2 subdeterminants zero (single dyadic) Planar = 0 ≠ 0 (single dyadic) ≠ 0; rank 2: at least one non-zero 2x2 subdeterminant Complete ≠ 0 ≠ 0 ≠ 0; rank 3: non-zero determinant Dyadics algebra Dyadic with vector
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DYADS - Dyad A is formed by two vectors a and b (complex in...

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