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math_LinearAlgebra_ner

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that O
basis O
its O
dimension O
can O
not O
be O
larger O
than O
m O
or O
n O
but O
it O
can O
be O
smalle O
consequently O
linear B-Math
algebra I-Math
algorithms O
have O
been O
highly O
optimize O
these O
operations O
and O
associated O
laws O
qualify O
euclidean O
vectors O
as O
an O
example O
of O
the O
more O
generalized O
concept O
of O
vectors O
defined O
simply O
as O
elements O
of O
a O
vector B-Math
space I-Math
a O
linear B-Math
map I-Math
from O
to O
always O
maps O
the O
origin O
of O
to O
the O
origin O
o O
in O
modern O
introductory O
texts O
on O
functional B-Math
analysis I-Math
the O
subject O
is O
seen O
as O
the O
study O
of O
vector O
spaces O
endowed O
with O
a O
topology O
in O
particular O
infinitedimensional O
space O
the O
subject O
is O
seen O
as O
the O