Tenney–Euclidean tuning: Difference between revisions
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* If ''A'' has rational entries, so does ''A''{{mpp}} | * If ''A'' has rational entries, so does ''A''{{mpp}} | ||
* {{nowrap|(''A''{{mpp}}){{mpp}} {{=}} ''A''}} | * {{nowrap|(''A''{{mpp}}){{mpp}} {{=}} ''A''}} | ||
* {{nowrap|(''A''{{ | * {{nowrap|(''A''{{t}}){{mpp}} {{=}} (''A''{{mpp}}){{t}}}}, where ''A''{{t}} is the transpose of ''A'' | ||
* ''AA''{{mpp}} is the orthogonal projection matrix that maps onto the space spanned by the columns of ''A'' | * ''AA''{{mpp}} is the orthogonal projection matrix that maps onto the space spanned by the columns of ''A'' | ||
* ''A''{{mpp}}''A'' is the orthogonal projection matrix that maps onto the space spanned by the rows of ''A'' | * ''A''{{mpp}}''A'' is the orthogonal projection matrix that maps onto the space spanned by the rows of ''A'' | ||