<s>
The	O
purpose	O
of	O
this	O
page	O
is	O
to	O
provide	O
supplementary	O
materials	O
for	O
the	O
ordinary	B-General_Concept
least	I-General_Concept
squares	I-General_Concept
article	O
,	O
reducing	O
the	O
load	O
of	O
the	O
main	O
article	O
with	O
mathematics	O
and	O
improving	O
its	O
accessibility	O
,	O
while	O
at	O
the	O
same	O
time	O
retaining	O
the	O
completeness	O
of	O
exposition	O
.	O
</s>
<s>
A	O
sufficient	O
condition	O
for	O
satisfaction	O
of	O
the	O
second-order	O
conditions	O
for	O
a	O
minimum	O
is	O
that	O
have	O
full	O
column	O
rank	O
,	O
in	O
which	O
case	O
is	O
positive	B-Algorithm
definite	I-Algorithm
.	O
</s>
<s>
When	O
is	O
positive	B-Algorithm
definite	I-Algorithm
,	O
the	O
formula	O
for	O
the	O
minimizing	O
value	O
of	O
can	O
be	O
derived	O
without	O
the	O
use	O
of	O
derivatives	O
.	O
</s>
<s>
By	O
using	O
a	O
Hermitian	B-Algorithm
transpose	I-Algorithm
instead	O
of	O
a	O
simple	O
transpose	O
,	O
it	O
is	O
possible	O
to	O
find	O
a	O
vector	O
which	O
minimizes	O
,	O
just	O
as	O
for	O
the	O
real	O
matrix	O
case	O
.	O
</s>
<s>
where	O
stands	O
for	O
Hermitian	B-Algorithm
transpose	I-Algorithm
.	O
</s>
<s>
By	O
properties	O
of	O
a	O
projection	B-Algorithm
matrix	I-Algorithm
,	O
it	O
has	O
p	O
=	O
rank(X )	O
eigenvalues	O
equal	O
to	O
1	O
,	O
and	O
all	O
other	O
eigenvalues	O
are	O
equal	O
to	O
0	O
.	O
</s>
<s>
where	O
is	O
the	O
symmetric	O
projection	B-Algorithm
matrix	I-Algorithm
onto	O
subspace	O
orthogonal	O
to	O
X	O
,	O
and	O
thus	O
MX	O
=	O
XM	O
=	O
0	O
.	O
</s>
