<s>
In	O
mathematics	O
,	O
Krawtchouk	B-Algorithm
matrices	I-Algorithm
are	O
matrices	B-Architecture
whose	O
entries	O
are	O
values	O
of	O
Krawtchouk	O
polynomials	O
at	O
nonnegative	O
integer	O
points	O
.	O
</s>
<s>
The	O
Krawtchouk	B-Algorithm
matrix	I-Algorithm
K(N )	O
is	O
an	O
matrix	O
.	O
</s>
<s>
The	O
first	O
few	O
Krawtchouk	B-Algorithm
matrices	I-Algorithm
are	O
:	O
</s>
<s>
As	O
a	O
transformation	B-Algorithm
,	O
a	O
Krawtchouk	B-Algorithm
matrix	I-Algorithm
is	O
an	O
involution	B-Algorithm
up	O
to	O
scaling	O
:	O
</s>
<s>
Krawchouk	O
matrices	B-Architecture
have	O
an	O
LDU	O
decomposition	O
involving	O
triangular	O
Pascal	B-Algorithm
matrices	I-Algorithm
and	O
a	O
diagonal	O
matrix	O
of	O
the	O
powers	O
of	O
2	O
.	O
</s>
