Deals with right angles.
all dimensions are orthogonal so there is no ranking them on distance.
Math Prelude: Orthogonal wave functions arise as a natural consequence of the mathematical structure of quantum mechanics and the relevant mathematical structure is called a Hilbert Space. Within this infinite dimensional (Hilbert) vector space is a definition of orthogonal that is exactly the same as "perpendicular" and that is the natural generalization of "perpendicular" vectors in ordinary three dimensional space. Within that context, wave functions are orthogonal or perpendicular when the "dot product" is zero. Quantum Answer: With that prelude, we can then say that mathematically, the collection of all quantum states of a quantum system defines a Hilbert Space. Two quantum functions in the space are said to be orthogonal when they are perpendicular and perpendicular means the "dot product" is zero. Physics Answer: The question asked has been answered, but what has not been answered (because it was not was not asked), is why orthogonal wave functions are important. As it turns out, anything that you can observe or measure about the state of a quantum system will be mathematically represented with Hermitian operators. A "pure" state, i.e. one where the same measurement always results in the same answers, is necessarily an eigenstate of a Hermtian operator and any two pure states that give two different results of measurement are necessarily "orthogonal wave functions." Conclusion: Thus, there are infinitely many orthogonal wave functions in the set of all wave functions of a quantum system and that orthogonal property has no physical meaning. When one identifies the subset of quantum states that associated pure quantum states (meaning specifically measured properties) and then two distinguishable measurement outcomes are associated with two different quantum states and those two are orthogonal. But, what was asked was a question of mathematics. Mathematically orthogonal wave functions do not guarantee distinct pure quantum state, but distinct pure quantum states does guarantee mathematically orthogonal wave functions. You can remember that in case someone asks.
Everything you've ever wanted to know can be found at the link below.
This is known as transverse(the plane orthogonal to the anteroposterior or oral-aboral axis.)
Solid barium chloride is obtained as orthogonal crystals (for the anhudrous salt).
Orthogonal signal space is defined as the set of orthogonal functions, which are complete. In orthogonal vector space any vector can be represented by orthogonal vectors provided they are complete.Thus, in similar manner any signal can be represented by a set of orthogonal functions which are complete.
The answer will depend on orthogonal to WHAT!
it is planning of orthogonal planning
it is planning of orthogonal planning
Orthogonal - novel - was created in 2011.
a family of curves whose family of orthogonal trajectories is the same as the given family, is called self orthogonal trajectories.
Orthogonal is a term referring to something containing right angles. An example sentence would be: That big rectangle is orthogonal.
Richard Askey has written: 'Three notes on orthogonal polynomials' -- subject(s): Orthogonal polynomials 'Recurrence relations, continued fractions, and orthogonal polynomials' -- subject(s): Continued fractions, Distribution (Probability theory), Orthogonal polynomials 'Orthogonal polynomials and special functions' -- subject(s): Orthogonal polynomials, Special Functions
Self orthogonal trajectories are a family of curves whose family of orthogonal trajectories is the same as the given family. This is a term that is not very widely used.
A matrix A is orthogonal if itstranspose is equal to it inverse. So AT is the transpose of A and A-1 is the inverse. We have AT=A-1 So we have : AAT= I, the identity matrix Since it is MUCH easier to find a transpose than an inverse, these matrices are easy to compute with. Furthermore, rotation matrices are orthogonal. The inverse of an orthogonal matrix is also orthogonal which can be easily proved directly from the definition.
Three of them are "orthogonal", "orthodontist", and "orthopedic", and "orthogonal" is a very important word in mathematics. For one example, two vectors are orthogonal whenever their dot product is zero. "Orthogonal" also comes into play in calculus, such as in Fourier Series.
Orthogonal view is basically seeing something in 2 dimensions that is actually 3 dimensions. The projection lines in these views are orthogonal to the projection plane which causes it to be 2 dimensions.