Self-adjoint operatorIn mathematics, a self-adjoint operator on an infinite-dimensional complex vector space V with inner product (equivalently, a Hermitian operator in the finite-dimensional case) is a linear map A (from V to itself) that is its own adjoint. If V is finite-dimensional with a given orthonormal basis, this is equivalent to the condition that the matrix of A is a Hermitian matrix, i.e., equal to its conjugate transpose A^∗. By the finite-dimensional spectral theorem, V has an orthonormal basis such that the matrix of A relative to this basis is a diagonal matrix with entries in the real numbers.
Modulation (music)In music, modulation is the change from one tonality (tonic, or tonal center) to another. This may or may not be accompanied by a change in key signature (a key change). Modulations articulate or create the structure or form of many pieces, as well as add interest. Treatment of a chord as the tonic for less than a phrase is considered tonicization. Modulation is the essential part of the art. Without it there is little music, for a piece derives its true beauty not from the large number of fixed modes which it embraces but rather from the subtle fabric of its modulation.
Equal temperamentAn equal temperament is a musical temperament or tuning system that approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, which gives an equal perceived step size, as pitch is perceived roughly as the logarithm of frequency.
FugueIn classical music, a fugue (fjuːɡ) is a contrapuntal, polyphonic compositional technique in two or more voices, built on a subject (a musical theme) that is introduced at the beginning in imitation (repetition at different pitches), which recurs frequently throughout the course of the composition. It is not to be confused with a fuguing tune, which is a style of song popularized by and mostly limited to early American (i.e. shape note or "Sacred Harp") music and West Gallery music.
Hyperspectral imagingHyperspectral imaging collects and processes information from across the electromagnetic spectrum. The goal of hyperspectral imaging is to obtain the spectrum for each pixel in the image of a scene, with the purpose of finding objects, identifying materials, or detecting processes. There are three general types of spectral imagers. There are push broom scanners and the related whisk broom scanners (spatial scanning), which read images over time, band sequential scanners (spectral scanning), which acquire images of an area at different wavelengths, and snapshot hyperspectral imagers, which uses a staring array to generate an image in an instant.
Image editingImage editing encompasses the processes of altering s, whether they are digital photographs, traditional photo-chemical photographs, or illustrations. Traditional analog image editing is known as photo retouching, using tools such as an airbrush to modify photographs or editing illustrations with any traditional art medium. Graphic software programs, which can be broadly grouped into vector graphics editors, raster graphics editors, and 3D modelers, are the primary tools with which a user may manipulate, enhance, and transform images.
DemosaicingA demosaicing (also de-mosaicing, demosaicking or debayering) algorithm is a used to reconstruct a full color image from the incomplete color samples output from an overlaid with a color filter array (CFA). It is also known as CFA interpolation or color reconstruction. Most modern digital cameras acquire images using a single image sensor overlaid with a CFA, so demosaicing is part of the required to render these images into a viewable format.
Elliptic operatorIn the theory of partial differential equations, elliptic operators are differential operators that generalize the Laplace operator. They are defined by the condition that the coefficients of the highest-order derivatives be positive, which implies the key property that the principal symbol is invertible, or equivalently that there are no real characteristic directions. Elliptic operators are typical of potential theory, and they appear frequently in electrostatics and continuum mechanics.
Imaging spectroscopyIn imaging spectroscopy (also hyperspectral imaging or spectral imaging) each pixel of an image acquires many bands of light intensity data from the spectrum, instead of just the three bands of the RGB color model. More precisely, it is the simultaneous acquisition of spatially in many spectrally contiguous bands. Some spectral images contain only a few s of a spectral data cube, while others are better thought of as full spectra at every location in the image.
Gottfried Wilhelm LeibnizGottfried Wilhelm (von) Leibniz ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is a prominent figure in both the history of philosophy and the history of mathematics. He wrote works on philosophy, theology, ethics, politics, law, history and philology. Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in probability theory, biology, medicine, geology, psychology, linguistics and computer science.
