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The parameters and variables of factor analysis can be given a geometrical interpretation. The data ( z a i {\displaystyle z_{ai}} ), the factors ( F p i {\displaystyle F_{pi}} ) and the errors ( ε a i {\displaystyle \varepsilon _{ai}} ) can be viewed as vectors in an N i {\displaystyle N_{i}} -dimensional Euclidean space (sample space), represented as z a {\displaystyle \mathbf {z} _{a}} , F p {\displaystyle \mathbf {F} _{p}} and ε a {\displaystyle {\boldsymbol {\varepsilon }}_{a}} respectively. Since the data are standardized, the data vectors are of unit length ( z a ⋅ z a = 1 {\displaystyle \mathbf {z} _{a}\cdot \mathbf {z} _{a}=1} ). The factor vectors define an N p {\displaystyle N_{p}} -dimensional linear subspace (. a hyperplane) in this space, upon which the data vectors are projected orthogonally. This follows from the model equation