Grassmann Algebra

TheInteriorProduct.nb 6
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6.12
� ���� 10: The interior product of two elements is congruent to the interior product of their
complements in reverse order.
The interior product of two elements is equal (apart from a possible sign) to the interior product
of their complements in reverse order.
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6.13
If the elements are of the same grade, the interior product of two elements is equal to the interior
product of their complements. (It will be shown later that, because of the symmetry of the
metric tensor, the interior product of two elements of the same grade is symmetric, hence the
order of the factors on either side of the equation may be reversed.)
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� ���� 11: An interior product with zero is zero.
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Every exterior linear space has a zero element whose interior product with any other element is
zero.
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� ���� 12: The interior product is distributive over addition.
The interior product is both left and right distributive over addition.
Orthogonality
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m r
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r m r m r
Orthogonality is a concept generated by the complement operation.
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