TI-Nspire seriesThe TI-Nspire is a graphing calculator line made by Texas Instruments, with the first version released in July 2007. The calculators feature a non-QWERTY keyboard and a different key-by-key layout than Texas Instruments's previous flagship calculators such as the TI-89 series. The original TI-Nspire was developed out of the TI PLT SHH1 prototype calculator (which itself was derived from the Casio ClassPad 300), the TI-92 series of calculators released in 1995, and the TI-89 series of calculators released in 1998.
TI-BASICTI-BASIC is the official name of a BASIC-like language built into Texas Instruments (TI)'s graphing calculators. TI-BASIC is a language family of three different and incompatible versions, released on different products: TI-BASIC 83 (on Z80 processor) for TI-83 series, TI-84 Plus series TI-BASIC 89 (on 68k processor) for TI-89 series, TI-92 series, Voyage 200 TI-BASIC Nspire (on ARM processor) for TI-Nspire and TI-Nspire CAS TI rarely refers to the language by name, but the name TI-BASIC has been used in some developer documentation.
Frame bundleIn mathematics, a frame bundle is a principal fiber bundle F(E) associated to any vector bundle E. The fiber of F(E) over a point x is the set of all ordered bases, or frames, for Ex. The general linear group acts naturally on F(E) via a change of basis, giving the frame bundle the structure of a principal GL(k, R)-bundle (where k is the rank of E). The frame bundle of a smooth manifold is the one associated to its tangent bundle. For this reason it is sometimes called the tangent frame bundle.
TI-83 seriesThe TI-83 series is a series of graphing calculators manufactured by Texas Instruments. The original TI-83 is itself an upgraded version of the TI-82. Released in 1996, it was one of the most popular graphing calculators for students. In addition to the functions present on normal scientific calculators, the TI-83 includes many features, including function graphing, polar/parametric/sequence graphing modes, statistics, trigonometric, and algebraic functions, along with many useful applications.
TI-92 seriesThe TI-92 series of graphing calculators are a line of calculators produced by Texas Instruments. They include: the TI-92 (1995), the TI-92 II (1996), the TI-92 Plus (1998, 1999) and the Voyage 200 (2002). The design of these relatively large calculators includes a QWERTY keyboard. Because of this keyboard, it was given the status of a "computer" rather than "calculator" by American testing facilities and cannot be used on tests such as the SAT or AP Exams while the similar TI-89 can be.
Constructive proofIn mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object. This is in contrast to a non-constructive proof (also known as an existence proof or pure existence theorem), which proves the existence of a particular kind of object without providing an example. For avoiding confusion with the stronger concept that follows, such a constructive proof is sometimes called an effective proof.
Eigenvalues and eigenvectorsIn linear algebra, an eigenvector (ˈaɪgənˌvɛktər) or characteristic vector of a linear transformation is a nonzero vector that changes at most by a constant factor when that linear transformation is applied to it. The corresponding eigenvalue, often represented by , is the multiplying factor. Geometrically, a transformation matrix rotates, stretches, or shears the vectors it acts upon. The eigenvectors for a linear transformation matrix are the set of vectors that are only stretched, with no rotation or shear.
Stiefel manifoldIn mathematics, the Stiefel manifold is the set of all orthonormal k-frames in That is, it is the set of ordered orthonormal k-tuples of vectors in It is named after Swiss mathematician Eduard Stiefel. Likewise one can define the complex Stiefel manifold of orthonormal k-frames in and the quaternionic Stiefel manifold of orthonormal k-frames in . More generally, the construction applies to any real, complex, or quaternionic inner product space.
Gauss–Bonnet theoremIn the mathematical field of differential geometry, the Gauss–Bonnet theorem (or Gauss–Bonnet formula) is a fundamental formula which links the curvature of a surface to its underlying topology. In the simplest application, the case of a triangle on a plane, the sum of its angles is 180 degrees. The Gauss–Bonnet theorem extends this to more complicated shapes and curved surfaces, connecting the local and global geometries. The theorem is named after Carl Friedrich Gauss, who developed a version but never published it, and Pierre Ossian Bonnet, who published a special case in 1848.
Eigendecomposition of a matrixIn linear algebra, eigendecomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors. Only diagonalizable matrices can be factorized in this way. When the matrix being factorized is a normal or real symmetric matrix, the decomposition is called "spectral decomposition", derived from the spectral theorem. Eigenvalue, eigenvector and eigenspace A (nonzero) vector v of dimension N is an eigenvector of a square N × N matrix A if it satisfies a linear equation of the form for some scalar λ.
