Composition algebra and Matrix ring

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Composition algebra and Matrix ring

Composition algebra vs. Matrix ring

In mathematics, a composition algebra over a field is a not necessarily associative algebra over together with a nondegenerate quadratic form that satisfies for all and in. In abstract algebra, a matrix ring is any collection of matrices over some ring R that form a ring under matrix addition and matrix multiplication.

Algebra over a field

In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product.

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Bicomplex number

In abstract algebra, a bicomplex number is a pair of complex numbers constructed by the Cayley–Dickson process that defines the bicomplex conjugate (w,z)^*.

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Biquaternion

In abstract algebra, the biquaternions are the numbers, where, and are complex numbers, or variants thereof, and the elements of multiply as in the quaternion group.

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Hurwitz's theorem (composition algebras)

In mathematics, Hurwitz's theorem is a theorem of Adolf Hurwitz (1859–1919), published posthumously in 1923, solving the Hurwitz problem for finite-dimensional unital real non-associative algebras endowed with a positive-definite quadratic form.

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Pauli matrices

In mathematical physics and mathematics, the Pauli matrices are a set of three complex matrices which are Hermitian and unitary.

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Quaternion

In mathematics, the quaternions are a number system that extends the complex numbers.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Split-complex number

In abstract algebra, a split complex number (or hyperbolic number, also perplex number, double number) has two real number components x and y, and is written z.

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Split-quaternion

In abstract algebra, the split-quaternions or coquaternions are elements of a 4-dimensional associative algebra introduced by James Cockle in 1849 under the latter name.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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