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orthogonal trajectories represent the curves in which the magnitude of the
velocity or the force is the same at each point on that curve. In the case of the flow field the orthognal
trajectories are called the velocity potential and in the case of Force Fileds the orthogonal trajectories are
called equipotential curves--curves in which the magnitude of the Force is the same.
What else can I help you with?
Show some details about the set of all orthogonal matrices?
The set of all orthogonal matrices consists of square matrices ( Q ) that satisfy the condition ( Q^T Q = I ), where ( Q^T ) is the transpose of ( Q ) and ( I ) is the identity matrix. This means that the columns (and rows) of an orthogonal matrix are orthonormal vectors. Orthogonal matrices preserve the Euclidean norm of vectors and the inner product, making them crucial in various applications such as rotations and reflections in geometry. The determinant of an orthogonal matrix is either ( +1 ) or ( -1 ), corresponding to special orthogonal matrices (rotations) and improper orthogonal matrices (reflections), respectively.
What is the definition of orthogonal signal space?
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.
Can the difference of 2 vectors be orthogonal?
The answer will depend on orthogonal to WHAT!
What is orthogonal planning in ancient Greece?
it is planning of orthogonal planning
When was Orthogonal - novel - created?
Orthogonal - novel - was created in 2011.
What is the orthogonal planning in ancient Greece?
it is planning of orthogonal planning
What is orthogonal lines?
Orthogonal lines are lines that intersect at a right angle, forming an angle of 90 degrees between them. In a Cartesian coordinate system, two lines are orthogonal if the product of their slopes is -1. This concept is often used in geometry, linear algebra, and various applications in physics and engineering. Orthogonality can also extend beyond lines to include vectors and functions in higher-dimensional spaces.
Self orthogonal trajectories?
a family of curves whose family of orthogonal trajectories is the same as the given family, is called self orthogonal trajectories.
How do you use Orthogonal in a sentence?
Orthogonal is a term referring to something containing right angles. An example sentence would be: That big rectangle is orthogonal.
What has the author Richard Askey written?
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
What is self orthogonal?
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.
Prove that the product of two orthogonal matrices is orthogonal and so is the inverse of an orthogonal matrix What does this mean in terms of rotations?
To prove that the product of two orthogonal matrices ( A ) and ( B ) is orthogonal, we can show that ( (AB)^T(AB) = B^TA^TA = B^T I B = I ), which confirms that ( AB ) is orthogonal. Similarly, the inverse of an orthogonal matrix ( A ) is ( A^{-1} = A^T ), and thus ( (A^{-1})^T A^{-1} = AA^T = I ), proving that ( A^{-1} ) is also orthogonal. In terms of rotations, this means that the combination of two rotations (represented by orthogonal matrices) results in another rotation, and that rotating back (inverting) maintains orthogonality, preserving the geometric properties of rotations in space.
