Digital Signal Processing Reference
In-Depth Information
M
−
1
[
C
]
[
I
][
V
]
=
V
=
In concrete terms, we get
14
3
a
b
M
−
1
−
M
−
1
2
3
=
(B.3)
−
2
which reduces to
a
b
M
−
1
−
2
3
=
We can compute the pseudo-inverse
M
−
1
and the final solution using the built-in MathScript
function
pinv
:
M = [1,4;3,-2];
P = pinv(M)
ans = P*[-2;3]
which yields
0
.
1429
0
.
2857
P
=
0
.
2143
−
0
.
0714
and therefore
a
b
0
.
1429
−
0
.
2857
2
3
=
0
.
2143
−
0
.
0714
which yields
a
= 0.5714 and
b
= -0.6429 which are the same as 4/7 and -9/14, respectively. A unique
solution is possible only when
M
is square and all rows linearly independent.(a linearly independent row
cannot be formed or does not consist solely of a linear combination of other rows in the matrix).
