Notation: For an
matrix
by
we mean the submatrix
of
which is obtained
by deleting the
row and
column.
The proof of the next theorem is omitted. The interested reader is advised to go through Appendix 14.3.
Recall that the dot product,
Which tells us,
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Note here that if
Let
Hence,
In general, for any
matrix
it can be proved that
is indeed equal to the volume of the
-dimensional
parallelopiped. The actual proof is beyond the scope of this book.