Linear independenceIn the theory of vector spaces, a set of vectors is said to be if there exists no nontrivial linear combination of the vectors that equals the zero vector. If such a linear combination exists, then the vectors are said to be . These concepts are central to the definition of dimension. A vector space can be of finite dimension or infinite dimension depending on the maximum number of linearly independent vectors. The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space is linearly dependent are central to determining the dimension of a vector space.
Vertical deflectionThe vertical deflection (VD) or deflection of the vertical (DoV), also known as deflection of the plumb line and astro-geodetic deflection, is a measure of how far the gravity direction at a given point of interest is rotated by local mass anomalies such as nearby mountains. They are widely used in geodesy, for surveying networks and for geophysical purposes. The vertical deflection are the angular components between the true zenith–nadir curve (plumb line) tangent line and the normal vector to the surface of the reference ellipsoid (chosen to approximate the Earth's sea-level surface).
Geodetic astronomyGeodetic astronomy or astronomical geodesy (astro-geodesy) is the application of astronomical methods into geodetic networks and other technical projects of geodesy. The most important applications are: Establishment of geodetic datum systems (e.g.
System of linear equationsIn mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. For example, is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by the ordered triple since it makes all three equations valid. The word "system" indicates that the equations should be considered collectively, rather than individually.
Linear mapIn mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a .
LongitudeLongitude (ˈlɒndʒᵻtjuːd, ˈlɒŋɡᵻ-) is a geographic coordinate that specifies the east–west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek letter lambda (λ). Meridians are imaginary semicircular lines running from pole to pole that connect points with the same longitude. The prime meridian defines 0° longitude; by convention the International Reference Meridian for the Earth passes near the Royal Observatory in Greenwich, south-east London on the island of Great Britain.
LinearityIn mathematics, the term linear is used in two distinct senses for two different properties: linearity of a function (or mapping ); linearity of a polynomial. An example of a linear function is the function defined by that maps the real line to a line in the Euclidean plane R2 that passes through the origin. An example of a linear polynomial in the variables and is Linearity of a mapping is closely related to proportionality. Examples in physics include the linear relationship of voltage and current in an electrical conductor (Ohm's law), and the relationship of mass and weight.
LinearizationIn mathematics, linearization is finding the linear approximation to a function at a given point. The linear approximation of a function is the first order Taylor expansion around the point of interest. In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations or discrete dynamical systems. This method is used in fields such as engineering, physics, economics, and ecology.
SI derived unitSI derived units are units of measurement derived from the seven SI base unit specified by the International System of Units (SI). They can be expressed as a product (or ratio) of one or more of the base units, possibly scaled by an appropriate power of exponentiation (see: Buckingham π theorem). Some are dimensionless, as when the units cancel out in ratios of like quantities.
Quadratic formIn mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, is a quadratic form in the variables x and y. The coefficients usually belong to a fixed field K, such as the real or complex numbers, and one speaks of a quadratic form over K. If , and the quadratic form equals zero only when all variables are simultaneously zero, then it is a definite quadratic form; otherwise it is an isotropic quadratic form.
Sonata formSonata form (also sonata-allegro form or first movement form) is a musical structure generally consisting of three main sections: an exposition, a development, and a recapitulation. It has been used widely since the middle of the 18th century (the early Classical period). While it is typically used in the first movement of multi-movement pieces, it is sometimes used in subsequent movements as well—particularly the final movement.
Similarity (geometry)In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection. This means that either object can be rescaled, repositioned, and reflected, so as to coincide precisely with the other object. If two objects are similar, each is congruent to the result of a particular uniform scaling of the other.
