Orthogonality - Wikipedia
In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity to the linear algebra of bilinear forms. Two elements u and v of a vector space with bilinear form are orthogonal when .
Orthogonality (mathematics) - Wikipedia
In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity to the linear algebra of bilinear forms. Two elements u and v of a vector space with bilinear form are orthogonal when .
Orthogonal coordinates - Wikipedia
In mathematics, orthogonal coordinates are defined as a set of d coordinates = (,, …,) in which the coordinate hypersurfaces all meet at right angles (note that superscripts are indices, not exponents).
Difference between Perpendicular, Orthogonal and Normal
2017年8月26日 · Here's an excerpt from Wikipedia (https://en.wikipedia.org/wiki/Orthogonality): In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.
orthogonal - Wiktionary, the free dictionary
2024年11月12日 · (geometry) Of two objects, at right angles; perpendicular to each other. A chord and the radius that bisects it are orthogonal. Of a pair of vectors: having a zero inner product; perpendicular. The normal vector and tangent vector at a given point are orthogonal. Of a square matrix: such that its transpose is equal to its inverse.
Orthogonality and Orthonormality | Brilliant Math & Science Wiki
In the same way, vectors are known as orthogonal if they have a dot product (or, more generally, an inner product) of \(0\) and orthonormal if they have a norm of \(1\). It turns out these two definitions are the same, and the connection between linear algebra and geometry quite strong.
orthogonality - What does it mean when two functions are "orthogonal …
2015年7月12日 · So intuitively, two orthogonal functions are functions that when multiplied result in a function that encloses the same area above and below the x axis. Another example of orthogonal functions are $sin(t)$ and $cos(4t)$. A plot of this is shown below too as a second plot. You can keep doing this to find orthogonal pairs of trigonometric functions.
What really is ''orthogonality''? - Mathematics Stack Exchange
2016年3月7日 · I know that we can define two vectors to be orthogonal only if they are elements of a vector space with an inner product. So, if x x → and y y → are elements of Rn R n (as a real vector space), we can say that they are orthogonal iff x ,y = 0 x →, y → = 0, where x ,y x →, y → is an inner product.
Orthogonal functions - Wikipedia
In mathematics, orthogonal functions belong to a function space that is a vector space equipped with a bilinear form. When the function space has an interval as the domain, the bilinear form may be the integral of the product of functions over the interval: ∫ ¯ d {\displaystyle \langle f,g\rangle =\int {\overline {f (x)}}g (x)\,dx.}
Orthogonality - Encyclopedia of Mathematics
2024年1月6日 · A generalization of the concept of perpendicularity of vectors in a Euclidean space. The most natural concept of orthogonality is put forward in the theory of Hilbert spaces. Two elements $ x $ and $ y $ of a Hilbert space $ H $ are said to be orthogonal $ ( x \perp y) $ if their inner product is equal to zero ( $ ( x, y) = 0 $). This concept ...