ABSTRACT
We now consider two n3 1 vectors v and w and an n3 n matrix A such that v¼Aw. The important assumption is made that the underlying information in this relation is preserved under rotation of the coordinate system. In particular, simple manipulation furnishes that
*M)
v0 ¼ Qv ¼ QAw ¼ QAQTQw ¼ QAQTw0 (3.1)
The square matrix A is now called a second-order tensor if and only if A0 ¼QAQT. Let A and B be second-order n3 n tensors. The manipulations below demon-
strate that AT, (AþB), AB, and A1 are likewise tensors.
