What is orthogonal?

Some articles on orthogonal:

Lauricella's Theorem
... In the theory of orthogonal functions, Lauricella's theorem provides a condition for checking the closure of a set of orthogonal functions, namely Theorem ... A necessary and sufficient condition that a normal orthogonal set be closed is that the formal series for each function of a known closed normal orthogonal set in terms of converge in the ...
Cubes - Orthogonal Projections
... The cube has four special orthogonal projections, centered, on a vertex, edges, face and normal to its vertex figure ... Orthogonal projections Centered by Face Vertex Coxeter planes B2 A2 Projective symmetry Tilted views ...
Stieltjes Transformation - Relationships To Orthogonal Polynomials
... If {Pn} is a sequence of orthogonal polynomials for this product, we can create the sequence of associated secondary polynomials by the formula It appears that is a Padé approximation of Sρ(z ... effective measure for transforming the secondary polynomials into an orthogonal system ...
Matrix (mathematics) - Square Matrices - Main Types - Orthogonal Matrix
... An orthogonal matrix is a square matrix with real entries whose columns and rows are orthogonal unit vectors (i.e ... Equivalently, a matrix A is orthogonal if its transpose is equal to its inverse which entails where I is the identity matrix ... An orthogonal matrix A is necessarily invertible (with inverse A−1 = AT), unitary (A−1 = A*), and normal (A*A = AA*) ...
Classical Group - Relationship With Bilinear Forms
... Bn = SO(2n + 1), the special orthogonal group of orthogonal (2n + 1)-by-(2n + 1) real matrices with determinant 1 ... Dn = SO(2n), the special orthogonal group of orthogonal 2n-by-2n real matrices with determinant 1 ... to drop the condition that the determinant be 1 and consider unitary groups and (disconnected) orthogonal groups ...

More definitions of "orthogonal":

  • (adj): Statistically unrelated.
  • (adj): Having a set of mutually perpendicular axes; meeting at right angles.
    Example: "Wind and sea may displace the ship's center of gravity along three orthogonal axes"
    Synonyms: rectangular