# The space of quadratic forms in the (n times m) array (Y) is a vector space of

## Question:

The space of quadratic forms in the \(n \times m\) array \(Y\) is a vector space of dimension \(m n(m n-1) / 2\). Exhibit a basis. Show that the four quadratic forms in Exercise 1.3 are invariant with respect to row and column permutations. Deduce that every invariant quadratic form is a linear combination of these four.

**Data From Exercise 1.3**

The \(F\)-ratio reported by anova (...) for treatment effects is not the ratio shown above. At least one is misleading for this design. Which one? Explain your reasoning.

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