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An augmented matrix is a matrix obtained by adjoining a row or column vector, or sometimes another matrix with the same vertical dimension. The most common use of an ...

Consider an infinite repository containing balls of n different types. Then the following table summarizes the number of distinct ways in which k balls can be picked for four ...

Various forms of opening and closing bracket-like delimiters are used for a number of distinct notational purposes in mathematics. The most common variants of bracket ...

The term "Cartan algebra" has two meanings in mathematics, so care is needed in determining from context which meaning is intended. One meaning is a "Cartan subalgebra," ...

A measure which takes values in the complex numbers. The set of complex measures on a measure space X forms a vector space. Note that this is not the case for the more common ...

Ellipses sharing common foci (left figure). The family of confocal ellipses covers the plane simply, in the sense that there is a unique ellipse passing through each point in ...

Hyperbolas sharing common foci (left figure). The family of confocal hyperbolas covers the plane simply, in the sense that there is a unique hyperbola passing through each ...

Geometric objects lying in a common plane are said to be coplanar. Three noncollinear points determine a plane and so are trivially coplanar. Four points are coplanar iff the ...

A sophisticated checksum (often abbreviated CRC), which is based on the algebra of polynomials over the integers (mod 2). It is substantially more reliable in detecting ...

The word "degree" has many meanings in mathematics. The most common meaning is the unit of angle measure defined such that an entire rotation is 360 degrees. This unit harks ...