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More specifically, they can be characterized as orthogonal matrices with determinant 1; that is, a square matrix R is a rotation matrix if and only if R T = R −1 and det R = 1. The set of all orthogonal matrices of size n with determinant +1 is a representation of a group known as the special orthogonal group SO( n ) , one example of which is ...
The standard form of the equation of a central conic section is obtained when the conic section is translated and rotated so that its center lies at the center of the coordinate system and its axes coincide with the coordinate axes. This is equivalent to saying that the coordinate system's center is moved and the coordinate axes are rotated to ...
Therefore, in computer algebra, normal form is a weaker notion: A normal form is a representation such that zero is uniquely represented. This allows testing for equality by putting the difference of two objects in normal form. Canonical form can also mean a differential form that is defined in a natural (canonical) way.
In general, a k-form is an object that may be integrated over a k-dimensional manifold, and is homogeneous of degree k in the coordinate differentials ,, …. On an n-dimensional manifold, a top-dimensional form (n-form) is called a volume form. The differential forms form an alternating algebra.
In differential geometry, a one-form (or covector field) on a differentiable manifold is a differential form of degree one, that is, a smooth section of the cotangent bundle. [1] Equivalently, a one-form on a manifold is a smooth mapping of the total space of the tangent bundle of to whose restriction to each fibre is a linear functional on the ...
The normalizer therefore has order p⋅(p − 1) and is known as a Frobenius group F p(p−1) (especially for p = 5), and is the affine general linear group, AGL(1, p). The Sylow p -subgroups of the symmetric group of degree p 2 are the wreath product of two cyclic groups of order p .