That is
MATLAB Is Case Sensitive. It is important to note that MATLAB is case sen-
sitive. That is, MATLAB distinguishes between upper- and lowercase letters. Thus,xand
Xare not the same variable. All function names must be in lowercase, such as inv(A),
eig(A), and poly(A).
Differentiation and Integration of Matrices. The derivative of an n*mmatrix
A(t)is defined to be the n*mmatrix, each element of which is the derivative of the
corresponding element of the original matrix, provided that all the elements aij(t)have
derivatives with respect to t. That is,
Similarly, the integral of an n*mmatrixA(t)is defined to be
Differentiation of the Product of Two Matrices. If the matrices A(t)andB(t)
can be differentiated with respect to t, then
Here again the multiplication of A(t)anddB(t)/dt[ordA(t)/dtandB(t)] is, in gener-
al, not commutative.
d
dt
[A(t)B(t)]=
dA(t)
dt
B(t)+A(t)
dB(t)
dt
G
3
a 11 (t) dt
3
a 12 (t) dt p
3
a 1 m(t) dt
3
a 21 (t) dt
3
a 22 (t) dt p
3
a 2 m(t) dt
oo o
3
an 1 (t) dt
3
a 2 n(t) dt p
3
anm(t) dt
W
3
A(t) dt=a
3
aij(t) dtb =
G
d
dt
a 11 (t)
d
dt
a 12 (t) p
d
dt
a 1 m(t)
d
dt
a 21 (t)
d
dt
a 22 (t) p
d
dt
a 2 m(t)
oo o
d
dt
an 1 (t)
d
dt
an 2 (t) p
d
dt
anm(t)
W
d
dt
A(t)= a
d
dt
aij(t)b =
A-^1 = C
2.2222 -0.1111 -0.8889
- 1.6667 0.3333 0.6667
0.2222 -0.1111 0.1111
S
880 Appendix C / Vector-Matrix AlgebraOpenmirrors.com