Nilpotent matrixIn linear algebra, a nilpotent matrix is a square matrix N such that for some positive integer . The smallest such is called the index of , sometimes the degree of . More generally, a nilpotent transformation is a linear transformation of a vector space such that for some positive integer (and thus, for all ). Both of these concepts are special cases of a more general concept of nilpotence that applies to elements of rings. The matrix is nilpotent with index 2, since .
Spectrum (functional analysis)In mathematics, particularly in functional analysis, the spectrum of a bounded linear operator (or, more generally, an unbounded linear operator) is a generalisation of the set of eigenvalues of a matrix. Specifically, a complex number is said to be in the spectrum of a bounded linear operator if either has no set-theoretic inverse; or the set-theoretic inverse is either unbounded or defined on a non-dense subset. Here, is the identity operator. By the closed graph theorem, is in the spectrum if and only if the bounded operator is non-bijective on .
Kernel (linear algebra)In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the linear subspace of the domain of the map which is mapped to the zero vector. That is, given a linear map L : V → W between two vector spaces V and W, the kernel of L is the vector space of all elements v of V such that L(v) = 0, where 0 denotes the zero vector in W, or more symbolically: The kernel of L is a linear subspace of the domain V.
April 23215 BC – A temple is built on the Capitoline Hill dedicated to Venus Erycina to commemorate the Roman defeat at Lake Trasimene. 599 – Maya king Uneh Chan of Calakmul attacks rival city-state Palenque in southern Mexico, defeating queen Yohl Ik'nal and sacking the city. 711 – Dagobert III succeeds his father King Childebert III as King of the Franks. 1014 – Battle of Clontarf: High King of Ireland Brian Boru defeats Viking invaders, but is killed in battle. 1016 – Edmund Ironside succeeds his father Æthelred the Unready as King of England.
Massive open online courseA massive open online course (MOOC muːk) or an open online course is an online course aimed at unlimited participation and open access via the Web. In addition to traditional course materials, such as filmed lectures, readings, and problem sets, many MOOCs provide interactive courses with user forums or social media discussions to support community interactions among students, professors, and teaching assistants (TAs), as well as immediate feedback to quick quizzes and assignments.
Distance educationDistance education, also known as distance learning, is the education of students who may not always be physically present at school, or where the learner and the teacher are separated in both time and distance. Traditionally, this usually involved correspondence courses wherein the student corresponded with the school via mail. Distance education is a technology-mediated modality and has evolved with the evolution of technologies such as video conferencing, TV, and the Internet.
AltiVecAltiVec is a single-precision floating point and integer SIMD instruction set designed and owned by Apple, IBM, and Freescale Semiconductor (formerly Motorola's Semiconductor Products Sector) — the AIM alliance. It is implemented on versions of the PowerPC processor architecture, including Motorola's G4, IBM's G5 and POWER6 processors, and P.A. Semi's PWRficient PA6T. AltiVec is a trademark owned solely by Freescale, so the system is also referred to as Velocity Engine by Apple and VMX (Vector Multimedia Extension) by IBM and P.
Cyclic groupIn group theory, a branch of abstract algebra in pure mathematics, a cyclic group or monogenous group is a group, denoted Cn, that is generated by a single element. That is, it is a set of invertible elements with a single associative binary operation, and it contains an element g such that every other element of the group may be obtained by repeatedly applying the group operation to g or its inverse. Each element can be written as an integer power of g in multiplicative notation, or as an integer multiple of g in additive notation.
MarchMarch is the third month of the year in both the Julian and Gregorian calendars. It is the second of seven months to have a length of 31 days. In the Northern Hemisphere, the meteorological beginning of spring occurs on the first day of March. The March equinox on the 20 or 21 marks the astronomical beginning of spring in the Northern Hemisphere and the beginning of autumn in the Southern Hemisphere, where September is the seasonal equivalent of the Northern Hemisphere's March.
Automatic vectorizationAutomatic vectorization, in parallel computing, is a special case of automatic parallelization, where a computer program is converted from a scalar implementation, which processes a single pair of operands at a time, to a vector implementation, which processes one operation on multiple pairs of operands at once. For example, modern conventional computers, including specialized supercomputers, typically have vector operations that simultaneously perform operations such as the following four additions (via SIMD or SPMD hardware): However, in most programming languages one typically writes loops that sequentially perform additions of many numbers.
April 1443 BC – Legions loyal to the Roman Senate, commanded by Gaius Pansa, defeat the forces of Mark Antony in the Battle of Forum Gallorum. 69 – Vitellius, commanding Rhine-based armies, defeats Roman emperor Otho in the First Battle of Bedriacum to take power over Rome. 966 – Following his marriage to the Christian Doubravka of Bohemia, the pagan ruler of the Polans, Mieszko I, converts to Christianity, an event considered to be the founding of the Polish state. 972 – Otto II, Co-Emperor of the Holy Roman Empire, marries Byzantine princess Theophanu.
