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

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Appendix I / Utilities / Matrices<br />

_ _<br />

( i : = [ 1(<br />

1 ) n ] ) ∧ ( j:<br />

= [ 1(<br />

1 ) m ] ) ⇒ bij<br />

: = a ij<br />

Equation 22.9-8<br />

M_I_IMAGE deals with an integer matrix [A(n,m)] in the same manner.<br />

22.9.5 Matrix Initialisation<br />

M_INITIAL takes constant (A) and returns matrix [B(n,m)] with its elements<br />

set to (A).<br />

22.9.6 Matrix Inversion<br />

M_INITIAL<br />

22.9-2<br />

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

( i : = [ 1(<br />

1 ) n ] ) ∧ ( j:<br />

= [ 1(<br />

1 ) m ] ) ⇒ bij<br />

: = a<br />

Equation 22.9-9<br />

Equation 22.9-10<br />

M_INVERSE inserts matrix [A(n,n)] where n ∈ [1(1)m] into the upper left<br />

partition of a matrix shell of dimension (m), returning the inverse of the<br />

partition in [B(n,n)].<br />

M_INVERSE<br />

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

( i : = [ 1(<br />

1 ) m ] ) ∧ ( j:<br />

= [ 1(<br />

1 ) m ] ) ⇒ [ B ] ≡ [ A ]<br />

22.9.7 Matrix Product<br />

Equation 22.9-11<br />

−1<br />

: =<br />

cof<br />

( a )<br />

ij<br />

det [ A ]<br />

Equation 22.9-12<br />

M_PRODUCT takes matrices [A(n,m)] and [B(m,p)], and returns their<br />

product in [C(n,p)].<br />

M_PRODUCT<br />

( i : = [ 1(<br />

1 ) n ] ) ∧ j:<br />

= [ 1(<br />

1 ) p ]<br />

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

Equation 22.9-13<br />

m<br />

( ) ⇒ c : = ( a ⋅ b )<br />

ij<br />

∑<br />

k:<br />

= p<br />

ik<br />

kj<br />

Equation 22.9-14

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