Concepts Flashcards

1
Q

Column vector

A

a
b
c

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2
Q

row vector

A

a, b, c

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3
Q

matrix element

A

aij

i row
j column

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4
Q

the diagonal of a matrix

A

aij
i=j

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5
Q

kM
scalar

A

ka, kb
kc, kd

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6
Q

add/minus need same dimension?

A

yes

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7
Q

C=AB

A

cij = k1->n aik bkj

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8
Q

multiplication [abstract sensation]

A

tilt -> drop
first top magnet

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9
Q

special matrix:

0
zero matrix

A

0 0
0 0

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10
Q

special matrix:

I
identity matrix

A

1 0 0
0 1 0
0 0 1

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11
Q

special matrix:

D
diagonal matrix

A

d1 0 0
0 d2 0
0 0 d3

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12
Q

special matrix:

B
band/banded matrix

A

d1 a1 0
b1 d2 a2
0 b2 d3

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13
Q

special matrix:

U
upper matrix

A

a b c
0 d e
0 0 f

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14
Q

special matrix:

L
lower matrix

A

a 0 0
b c 0
d e f

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15
Q

what is transpose?

A

diagonal flip

aij -> aji

mxn -> nxm

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16
Q

A is symmetric if …

A

AT = A

e.g.

a b c
b d e
c e f

17
Q

if AT = A, then A is …

A

symmetric

“square flip”
e.g.

a b c
b d e
c e f

18
Q

if AT = - A, then A is …

A

skew symmetric

e.g.

0 b c
-b 0 e
-c -e 0

19
Q

A is skew symmetric if …

A

AT = - A

0 b c
-b 0 e
-c -e 0