Matrix Form of Tensor Transformations

Tensors can easily be written in matrix form. For example, a vector aj can be represented with a column matrix  

A fourth-order tensor can be written as a 9x9 array in analogy to Equation (A.51) but, by use of contracted notation, is sometimes drastically simplified to a 6 x 6 symmetric array. 

A-1 Stephen W. Tsai, Mechanics of Composite Materials, Part II, Theoretical Aspects, Air Force Materials Latx ratory Technical Report, AFML-TR-66-149, November 1966. 

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