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Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

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Appendix I / Utilities / Vectors<br />

_ _<br />

22.12.15 Vector Zero<br />

y : = V_3_PRODUC T<br />

( A , B , C , k , m , n ) : = ( a ⋅ b ⋅ c )<br />

22.12-5<br />

m<br />

∑<br />

i:<br />

= k<br />

i<br />

Equation 22.12-29<br />

V_ZERO takes vector (A) of dimension (n), and returns the same vector<br />

with elements [1 ≤ k (1) m ≤ n] set to zero.<br />

22.12.16 Vector Summation<br />

V_ZERO<br />

( A , k , m , n )<br />

[ k ( 1 ) m ] ⇒ a : 0<br />

i ∈<br />

i =<br />

[ k ( 1 ) m ] ⇒ ai<br />

: ai<br />

i ∉<br />

=<br />

Equation 22.12-30<br />

Equation 22.12-31<br />

Equation 22.12-32<br />

V_SUM takes vector (A) of dimension (n), and returns the sum of its<br />

elements [1 ≤ k (1) m ≤ n].<br />

y : = V_SUM<br />

22.12.17 Vector Extraction from a Matrix<br />

m<br />

∑<br />

i : = k<br />

( A , k , m , n ) : = ( a )<br />

i<br />

Equation 22.12-33<br />

V_M_EXTRACT takes matrix [A(m,n)] and returns the row and column<br />

vectors (B) and (C) of dimension (n) and (m) identified by the indices (i)<br />

and (j) respectively where (i ∈ [1 (1) m] ) and (j ∈ [1 (1) n] ).<br />

Row extraction,<br />

V_M_EXTRAC T<br />

( [ A ] , B , C , i , j , m , n )<br />

[ 1(<br />

1 ) n ] ⇒ bk<br />

: a i,<br />

k<br />

∀ k ∈<br />

=<br />

Equation 22.12-34<br />

Equation 22.12-35<br />

i<br />

i

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