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In mathematics, specifically multilinear algebra, a dyadic or dyadic tensor is a second order tensor, written in a notation that fits in with vector algebra. There are numerous ways to multiply two Euclidean vectors. The dot product takes in two vectors and returns a scalar, while the cross product returns a pseudovector. Both of these have various significant geometric interpretations and are widely used in mathematics, physics, and engineering. The dyadic product takes in two vectors and returns a second order tensor called a ''dyadic'' in this context. A dyadic can be used to contain physical or geometric information, although in general there is no direct way of geometrically interpreting it. The dyadic product is linear in both of its operands (in other words, two dyadics can be added to get another dyadic, and multiplied by numbers to scale the dyadic), and distributive over vector addition. However, it is not commutative; changing the order of the vectors results in a different dyadic. It is associative with scalar multiplication, and even with the dot and cross products with other vectors. The formalism of dyadic algebra is an extension of vector algebra to include the dyadic product of vectors, and the dot, cross, and dyadic products can be combined together to obtain other scalars, vectors, or dyadics. It also has some aspects of matrix algebra, as the numerical components of vectors can be arranged into row and column vectors, and those of second order tensors in square matrices. Also, the dot, cross, and dyadic products can all be expressed in matrix form. Dyadic expressions closely resemble the matrix equivalents. The dot product of a dyadic with a vector gives another vector, and taking the dot product of this result gives a scalar derived from the dyadic. The effect that a given dyadic has on other vectors can provide indirect physical or geometric interpretations. Dyadic notation was first established by Josiah Willard Gibbs in 1884. The notation and terminology are relatively obsolete today. Its uses in physics include continuum mechanics and electromagnetism. In this article, upper-case bold variables denote dyadics (including dyads) whereas lower-case bold variables denote vectors. An alternative notation uses respectively double and single over- or underbars. ==Definitions and terminology== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Dyadics」の詳細全文を読む スポンサード リンク
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