Notation

Accents¶

• $\mathbf{x}$ (bold, non-italic typeface) Matrix or vector

• $x$ (non-bold, italic typeface) Scalar or array

Variables¶

• $n_f$ Number of frequency lines

• $n_c$ Number of control channels

• $n_o$ Number of output signals

• $n_s$ Number of samples in a signal

• $n_{os}$ Number of samples in an oversampled output signal

• $\mathbf{G}_{vv}$ CPSD matrix for the output signals

• $\mathbf{G}_{xx}$ CPSD matrix for the responses (i.e. the specification)

• $\mathbf{H}_{xv}$ Transfer function matrix between the responses and the output signals

• $\mathbf{X}$ Response spectra (FFT)

• $\mathbf{V}$ Output spectra (FFT)

• $\mathbf{T}$ Transformation matrix

• $\mathbf{A}$ State or system matrix for state space equations of motion

• $\mathbf{B}$ Input matrix for state space equations of motion

• $\mathbf{C}$ Output matrix for state space equations of motion

• $\mathbf{D}$ Feedthrough or feedforward matrix for state space equations of motion

• $\mathbf{x}$ State vector for state space equations of motion

• $\mathbf{y}$ Output vector for state space equations of motion

• $\mathbf{u}$ Input vector for state space equations of motion

• $\mathbf{M}$ Mass matrix for 2nd-order differential equations of motion

• $\mathbf{C}$ Damping matrix for 2nd-order differential equations of motion

• $\mathbf{K}$ Stiffness matrix for 2nd-order differential equations of motion

Operations¶

• ⬚$^+$ Pseudoinverse of a matrix

• ⬚$^H$ Complex-conjugate transpose of a matrix (hermitian)