The analogy between ANOVA for general n-factor crossed layouts and the ANOVA-type decomposition of square integrable statistics is demonstrated using the notions and notations of tensor analysis and multilinear algebra. A theory of tensors is developed in such a way that (a) it can be immediately applied in computer programs, and (b) it can be easily generalized to L 2 spaces.
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Akimichi Takemura (1983) studied this question.
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