Binary, Permutation, and Communication Matrices (VCE SSCE General Mathematics): Flashcards

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Binary, Permutation, and Communication Matrices
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Binary matrix

Matrix containing only 0 and 1

Permutation matrix structure

Square matrix, one 1 per row/column, rest 0s

Meaning of 'permutation'

Rearrangement

Pre-multiplying with PP

Forming product PimesXP imes X (PP comes first)

Post-multiplying with PP

Forming product XimesPX imes P (PP comes second)

Inverse of permutation matrix PP

P1=PTP^{-1} = P^T (inverse equals transpose)

Communication matrix

Square binary matrix showing direct links in network

Finding two-step communication links

Square the communication matrix (C2C^2)

Redundant communication links

Links where sender and receiver are same person

Total one-step and two-step links

T=C+C2T = C + C^2

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