Last Updated：2025/12/30
Sentence
The
linear
independence
of
a
set
of
vectors
can
be
determined
by
calculating
the
Gram
determinant
of
those
vectors;
if
their
Gram
determinant
is
zero,
then
they
are
linearly
dependent,
and
if
their
Gram
determinant
is
non-zero,
then
they
are
linearly
independent.
Incidentally,
the
same
Gram
determinant
can
be
used
to
calculate
the
hyper-volume
of
a
hyper-parallelepiped
(whose
edges
which
"radiate"
from
an
"origin"
vertex
are
described
by
the
vectors).
Quizzes for review
The linear independence of a set of vectors can be determined by calculating the Gram determinant of those vectors; if their Gram determinant is zero, then they are linearly dependent, and if their Gram determinant is non-zero, then they are linearly independent. Incidentally, the same Gram determinant can be used to calculate the hyper-volume of a hyper-parallelepiped (whose edges which radiate
from an origin
vertex are described by the vectors).
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