Back Matter

Abstract

Adjoint-For a finite-dimensional linear map (i.e., a matrix A), the adjoint A * is given by the complex conjugate transpose of the matrix. In the infinite-dimensional context, the adjoint * of a linear operator is defined so that 〈〈 f , g 〉 = 〈 f , * g 〉, where 〈·, ·〉 is an inner product. Closed-loop control-A control architecture where the actuation is informed by sensor data about the output of the system. Coherent structure-A spatial mode that is correlated with the data from a system. Compressed sensing-The process of reconstructing a high-dimensional vector signal from a random undersampling of the data using the fact that the high-dimensional signal is sparse in a known transform basis, such as the Fourier basis. Compression-The process of reducing the size of a high-dimensional vector or array by approximating it as a sparse vector in a transformed basis. For example, MP3 and JPG compression use the Fourier basis or wavelet basis to compress audio or image signals. Control theory-The framework for modifying a dynamical system to conform to desired engineering specifications through sensing and actuation. Data matrix-A matrix where each column vector is a snapshot of the state of a system at a particular instant in time. These snapshots may be sequential in time, or they may come from an ensemble of initial conditions or experiments. DMD amplitude-The amplitude of a given DMD mode as expressed in the data. These amplitudes may be interpreted as the significance of a given DMD mode, similar to the power spectrum in the FFT. DMD eigenvalues-Eigenvalues of the best-fit DMD operator A (see dynamic mode decomposition) representing an oscillation frequency and a growth or decay term. DMD mode (also dynamic mode)-An eigenvector of the best-fit DMD operator A (see dynamic mode decomposition). These modes are spatially coherent and oscillate in time at a fixed frequency and a growth or decay rate. Dynamic mode decomposition (DMD)-The leading eigendecomposition of a best-207