Why?

Wind turbines are examined as dynamic systems in Wind II and these notes provide the basis of dynamic analysis. You will not however be expected to manipulate matrices as part of the course.

What?

Notation:

Matrices are denoted by bold capitals, A, M; while elements/components of matrix are denoted by lower case with subscripts.

For example:

is an m by n matrix, (m x n).

Lower case bold is used for column or row vectors (matrices with one of the dimensions equal to unity), eg u, v, x y.

For square matrices:

The determinant of M (det M) is written ιMι
The transpose of A is A^T, ie a_ij ↔a_ji
M is singular if ιMι= 0, otherwise non-singular
Inverse of A for non-singular matrices is denoted A^-1 such that AA^-1= , the unit matrix .
A matrix M is symmetric if MT = M
If MT = -M, then the matrix is skew-symmetric.