Concepts Flashcards
Column vector
a
b
c
row vector
a, b, c
matrix element
aij
i row
j column
the diagonal of a matrix
aij
i=j
kM
scalar
ka, kb
kc, kd
add/minus need same dimension?
yes
C=AB
cij = k1->n aik bkj
multiplication [abstract sensation]
tilt -> drop
first top magnet
special matrix:
0
zero matrix
0 0
0 0
special matrix:
I
identity matrix
1 0 0
0 1 0
0 0 1
special matrix:
D
diagonal matrix
d1 0 0
0 d2 0
0 0 d3
special matrix:
B
band/banded matrix
d1 a1 0
b1 d2 a2
0 b2 d3
special matrix:
U
upper matrix
a b c
0 d e
0 0 f
special matrix:
L
lower matrix
a 0 0
b c 0
d e f
what is transpose?
diagonal flip
aij -> aji
mxn -> nxm
A is symmetric if …
AT = A
e.g.
a b c
b d e
c e f
if AT = A, then A is …
symmetric
“square flip”
e.g.
a b c
b d e
c e f
if AT = - A, then A is …
skew symmetric
e.g.
0 b c
-b 0 e
-c -e 0
A is skew symmetric if …
AT = - A
0 b c
-b 0 e
-c -e 0
