N',m, il-(--w] ,f 'E f r rj Zx3 hrL j h{ON = e a - - PDF document

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N',m, il-(--w] ,f 'E f r rj Zx3 hrL j h{ON = e a - - PDF document

Dec 01, 2023 7 likes •61 views

-q .;.***v i..,'..:: ,,:,,': ,..,,,; ,. (3 Affine Ti'ansformations I 3) 4lrt'a^1 sdd{, done- or) W{dne t! 7-'-J{ l'{orch v1.t (Mccenn)- p. M|trlr- CSc 245 15 (1 Zero-One Matrices / 3) Three Operations: 'Jgin': (t y O)

slide-1
SLIDE 1
  • q
.;.***v

i..,'..:: ,,:,,': ,. ,..,,,; Affine Ti'ansformations (3 I 3)

W{dne sdd{,

done- or)

7-'-J{ t!

4lrt'a^1

l'{orch

M|trl€r- CSc 245 v1.t (Mccenn)- p. 15

Zero-One Matrices (1 / 3)

Three Operations: 1. 'Jgin': (t y O)

2. !(eet': tA I b)

, ,,/lftQ'dndatr'

1{:til*'E

il H'-=[il

MlN"

c)

\

O

I

  • irariG-
CSc 2i+5 v1.1 (Mccann)
  • p.
16
slide-2
SLIDE 2

Tero-One Matrices (2 / 3)

( t;u . brj) 3. 'Boolean Product': hmider A [ynr.n) and S (n x [) C = AOS is mr r -[ whor.u .,J = { (n,u A b".)

;:,1 ;,;,,.:r;,1 l:::l: ,:::,.:::', .::.,'', i h-t l

il-(--w] N',m, ,f

f r rj 'E

hrL Zx3

a

g*5

j h{ON = e

(o nl\vto^o)"o t 0

nojv(o,t\)=O I t

  • tl

f\

n.- <)

'[: 4

lr= |

lrd.is- CSo 245 vl.1 {McCann)
  • S'17

Zero-One Matrices (3 | 3)

Definitio n: rth Boolean Power

W fl bootran pquf q{ 4n A Lftttl) rs *trr n(n nnqh*

guctessl\N. bm\Wr Pro&rc*s .

NKrt O I

, r l \

rt$u\ttrrg {Yorn na4rlf

r- [ Aft ' 4to1 i

hoA

I.,

lffiic€s - GSc 245 vl .l {Mccann)
  • p. 1
I
slide-3
SLIDE 3

Topic 8:

Relations

Rslalions- csa 245 v1,1 (Mccanfl)- D 1

Background

Having collections

  • f

data: Good, Knowing the connections between collections: Better!

, : , , . . '

Shd rdg tout"sts Dqt Trces lJe[ftrn ^ gC Qrv^au>

Reldh{ls - CSc ?45 v1,1 {McCenn)- p. 2
slide-4
SLIDE 4

Relations (1 | 2)

Definition: (Binary) Relation

ftor # [ ilo *r Y \: t 2 h"] * ll,* t*Uy\a^ (N(

  • t-

X {}fu doru,nln\ d},,A Y ( lltucdon ain),

F

h--rl/urwd\ #hn:on' Ui r,u{r) (,u,kq &% n lrrl)*ocr*.,lyMW

'f

ff e A r h = Z(LatwlT r0e*occau), 6 ril^rd trn)' [c'R)' (t'qryot'rRo V'b\

Rd8liofl8- CSc ?45 vl.l (Mccann)
  • p,
3

Relations (2 | 2)

Definition: Related

[' krV)eK , x i: re\a ,rY

(xKY) '

tD Y*^v)e A

Ifu,nrrudt r$c*o crnY Mnuh KVzrrr:cr^\-

(ltonnutyrkte\;(niL k (

t^,rtt r !- vnl *11 ""0')

Relali(rc - CSc 245 vl.r Nccam) - p, 4
slide-5
SLIDE 5

Graph Representations

  • f

Relations (1 | 2)

Recall:

A-.- B,- R*

Presidents-Parties {Kennedy, Johnson, Nixon, Carter, Reagan} {Dem, Rep} {1rcennedy, Dem), (Johnson, Dem), (Nixon,Rep), (Carter, Dem), (Reagan, Rep) )

Kennedyl , Johnson . *?; Democratic Nixon.\1 Carter.y' )gn"publican Reagan. <

Rdatiom-CSc245 v1.1 (McCm)-p 5

Graph Representations

  • f

Relations (2 | 2)

r%a-A,n*yk.

Recall: H - {I,2,3,4,,5,6}? R * {(2, 1), (3, 1), (4, 1), (5, 1), (6, 1) , (4,2), (6,2), (6, 3)}

Rdafm
  • CSc 245 v1.1 (McCEnn)
  • p. 6