Define orthogonally

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WebAn n × n matrix is called orthogonally diagonalizable if there is an orthogonal matrix U and a diagonal matrix D for which A = U D U − 1 = U D U ⊤. Thus, an orthogonally … WebThe Spectral Theorem: An n n matrix is orthogonally diagonalizable if and only if it is symmetric. Definition: Let A be an n n matrix. We say that A is orthogonally diagonalizable if either of the two equivalent conditions holds: 1. There exists an orthogonal matrix S such that S 1AS is diagonal; 2. A has an orthonormal eigenbasis.

Usage of the word "orthogonal" outside of mathematics

Web1.2.1. Linear Independence vs Orthogonality#. If \(X \subset \mathbb R^n\) is an orthogonal set and \(0 \notin X\), then \(X\) is linearly independent.. Proving this is a nice exercise. While the converse is not true, a kind of partial converse holds, as we’ll see below.. 1.3. Weborthogonal: [adjective] intersecting or lying at right angles. having perpendicular slopes or tangents at the point of intersection. roscher physiotherapy

ORTHOGONAL English meaning - Cambridge Dictionary

WebSep 17, 2024 · The preview activity dealt with a basis of R2 formed by two orthogonal vectors. We will more generally consider a set of orthogonal vectors, as described in the next definition. Definition 6.3.1. By an orthogonal set of vectors, we mean a set of nonzero vectors each of which is orthogonal to the others. WebOrthogonally definition: In an orthogonal manner; perpendicularly ; at right angles. Webnoun. : a system of curves or surfaces consisting of two families whose components where they intersect are mutually perpendicular (as the lines of force and the … storage of oral interferon

What does orthogonal mean in biology? - Quora

7.4: Orthogonality - Mathematics LibreTexts

Weborthogonal ( ɔːˈθɒɡənəl) adj 1. (Mathematics) relating to, consisting of, or involving right angles; perpendicular 2. (Mathematics) maths a. (of a pair of vectors) having a defined … WebSep 17, 2024 · Recall from Definition 4.11.4 that non-zero vectors are called orthogonal if their dot product equals \(0\). A set is orthonormal if it is orthogonal and each vector is a unit vector. ... In this case, we say that \(A\) is orthogonally diagonalizable. Therefore every symmetric matrix is in fact orthogonally diagonalizable. The next theorem ... roscher fine porcelain soup bowlsWeborthogonal. adj. 1 relating to, consisting of, or involving right angles; perpendicular. 2 (Maths) a (of a pair of vectors) having a defined scalar product equal to zero. b (of a pair of functions) having a defined product equal to zero. ♦ orthogonally adv. storage of paperwhite bulbs

"WebAn orthogonal matrix Q is necessarily invertible (with inverse Q−1 = QT ), unitary ( Q−1 = Q∗ ), where Q∗ is the Hermitian adjoint ( conjugate transpose) of Q, and therefore normal ( Q∗Q = QQ∗) over the real numbers. The determinant of any orthogonal matrix is either +1 or −1. As a linear transformation, an orthogonal matrix ... " - Define orthogonally

Define orthogonally

Orthogonally Additive Operators on Vector Lattices SpringerLink

Orthogonality in programming language design is the ability to use various language features in arbitrary combinations with consistent results. This usage was introduced by Van Wijngaarden in the design of Algol 68: The number of independent primitive concepts has been minimized in order that the language be easy to describe, to learn, and to implement. On the other hand, these concepts have been appl… Orthogonality in programming language design is the ability to use various language features in arbitrary combinations with consistent results. This usage was introduced by Van Wijngaarden in the design of Algol 68: The number of independent primitive concepts has been minimized in order that the language be easy to describe, to learn, and to implement. On the other hand, these concepts have been appl… WebThe similarity relationship between the test and standard words varied orthogonally in terms of type of similarity and position of overlap. From the Cambridge English Corpus …

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WebApr 7, 2013 · ORTHOGONAL. By N., Sam M.S. 1. alone, separate or unrelated. 2. at 90 degree angles. ORTHOGONAL: "The orthogonal aspects of the buildings was majorly to credit for the impression the architecture gave when filmed." http://www.math.lsa.umich.edu/~kesmith/SpectralTheoremW2024.pdf

WebMay 18, 2024 · Adjacent Orthogonally or diagonally adjacent; share at least one common vertex; has a Chebyshev distance of 1. Orthogonally adjacent, neighboring …

WebWhen a matrix P is orthogonal, then its columns are not just a basis for Rn, they are an orthonormal basis. The fact that A is orthogonally diagonalisable means that, for A, you don't have to choose! The columns of P are both an orthonormal basis, and a basis of eigenvectors for A. So you get the best of both worlds. WebFeb 10, 2011 · In statistics, the meaning of orthogonal as unrelated (or more precisely uncorrelated) is very directly related to the mathematical definition. [Two vectors x and y …

WebDefine orthogonality. orthogonality synonyms, orthogonality pronunciation, orthogonality translation, English dictionary definition of orthogonality. adj. 1. Relating to or composed of right angles. 2. Mathematics a. Of or relating to a matrix whose transpose equals its inverse. ... Orthogonally-Multiplexed Orthogonal Phase Modulation ...

Weba. Of or relating to a matrix whose transpose equals its inverse. b. Of or relating to a linear transformation that preserves the length of vectors. 3. Very different or unrelated; … storage of ovenwareWeborthogonal adjective mathematics specialized uk / ɔːˈθɒɡ. ə n. ə l / us / ɔːˈθɑː.ɡ ə n. ə l / relating to an angle of 90 degrees, or forming an angle of 90 degrees SMART … storage of patient recordsWeborthogonality, In mathematics, a property synonymous with perpendicularity when applied to vectors but applicable more generally to functions. Two elements of an inner product … storage of pfaWeborthogonally ý nghĩa, định nghĩa, orthogonally là gì: 1. in a way that forms, resembles, or relates to an angle of 90 degrees: 2. in a way that forms…. Tìm hiểu thêm. storage of our brainWeborthogonal: The term orthogonal is derived from the Greek orthogonios ("ortho" meaning right and "gon" meaning angled ). Orthogonal concepts have origins in advanced … storage of outdoor cushionsWebAn orthogonal matrix is a square matrix A if and only its transpose is as same as its inverse. i.e., A T = A-1, where A T is the transpose of A and A-1 is the inverse of A. From this definition, we can derive another definition of an orthogonal matrix. Let us see how. A T = A-1. Premultiply by A on both sides, AA T = AA-1,. We know that AA-1 = I, where I … storage of onions refrigeratorWeborthogonally (comparative more orthogonally, superlative most orthogonally) In an orthogonal manner; perpendicularly; at right angles. 1968, Adriaan van Wijngaarden et … storage of oxygen concentrator