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What else can I help you with?
Can the difference of 2 vectors be orthogonal?
The answer will depend on orthogonal to WHAT!
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.
What does the mean of product of two orthogonal matrix is orthogonal in terms of rotation?
The mean of the product of two orthogonal matrices, which represent rotations, is itself an orthogonal matrix. This is because the product of two orthogonal matrices is orthogonal, preserving the property that the rows (or columns) remain orthonormal. When averaging these rotations, the resulting matrix maintains orthogonality, indicating that the averaged transformation still represents a valid rotation in the same vector space. Thus, the mean of the rotations captures a new rotation that is also orthogonal.
What is a vector which is orthogonal to the other vectors and is coplanar with the other vectors called?
In a plane, each vector has only one orthogonal vector (well, two, if you count the negative of one of them). Are you sure you don't mean the normal vector which is orthogonal but outside the plane (in fact, orthogonal to the plane itself)?
If you is orthogonal to v and w then is u orthogonal to v plus w?
yes. not sure of the proof though.
Self orthogonal trajectories?
a family of curves whose family of orthogonal trajectories is the same as the given family, is called self orthogonal trajectories.
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.
Why use orthogonal trajectories?
we dont ever
What are the Applications of orthogonal trajectory?
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 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
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 an orthogonal matrix?
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.
