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

Glossary
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0.9 Matrix Operators
[ M ] Square brackets are used to denote matrices (optional)
( i , j )
m The component in the i’th row and j’th column of [M]
[ A ] ⋅ [ B ] Matrix product of matrices [A] and [B]
[ A ] ⊗ [ B ] Element by element multiplication of matrices [A] and [B]
det [ M ] Determinant of matrix [M]
tr [ M ] Trace of matrix [M]
[ ] T
M Transpose of matrix [M]
[ ] 1
M − Inverse of matrix [M], defined ⇔ det [M] ≠ 0.
M Matrix-2 norm of a matrix [M]
L2
M Frobenius norm of a matrix [M]
F
U [ M ] The upper triangular matrix extracted from matrix [M]
including the main diagonal
L [ M ] The lower triangular matrix extracted from matrix [M]
excluding the main diagonal
0.10 Quaternion Operators
B
Q A Quaternion representing the orientation of frame (B) with
respect to frame (A)
C
B
B
A
Q Q ⊗ Quaternion product
( ) * B
Q Quaternion transposition equivalent to A
Q
A
0.11 Uncertainty and Covariance Operators
A Auto-covariance of random variable (A)
A , B Cross-covariance of random variable (A,B)
E ( A)
Expectation operator acting on variable (A)
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B