# Orthogonality from infinitesimal small rotation

• Warlord_
In summary, the first equation states that the length of a vector remains unchanged under rotations. The second equation is derived from the first using the chain rule and assuming a delta value of gik. The third equation is asking for clarification on the chain rule and whether vik is time dependent and equal to I for infinitely small matrices.
Warlord_
Hello buddies,

Thanks,

Um... Ok, it's a little difficult to know what level of detail you want.

The first equation essentially says that the length of a vector does not change under rotations. The second one follows from the first one using the chain rule, and assuming delta of gik is zero.

gik is basically the inner product of the base set vector, i.e., <ei,ek>.
- Could you please explicit the chain rule?
- is vik time dependent? And since it is an infinitely small matrix, the ##\delta v^k_i = I##?

Thanks

## What is orthogonality from infinitesimal small rotation?

Orthogonality from infinitesimal small rotation is a concept in mathematics and physics that describes the relationship between two objects or vectors that are rotated by a very small amount. It is used to determine if two objects are perpendicular or at right angles to each other.

## How is orthogonality from infinitesimal small rotation calculated?

To calculate orthogonality from infinitesimal small rotation, we use the dot product formula, which multiplies the components of two vectors and adds them together. If the result is zero, the two vectors are orthogonal. This calculation is repeated for a very small rotation to determine the degree of orthogonality between the two objects.

## What is the importance of orthogonality from infinitesimal small rotation?

Orthogonality from infinitesimal small rotation is important in many fields, including mathematics, physics, engineering, and computer science. It allows us to determine the relationship between two objects or vectors and can be used to solve problems involving rotations, forces, and geometric shapes.

## Are there any real-world applications of orthogonality from infinitesimal small rotation?

Yes, there are many real-world applications of orthogonality from infinitesimal small rotation. For example, it is used in robotics to determine the orientation of objects and in computer graphics to create realistic 3D models. It is also important in physics for calculating forces and torques on objects.

## Can orthogonality from infinitesimal small rotation be applied to non-Euclidean spaces?

No, orthogonality from infinitesimal small rotation is only applicable in Euclidean spaces, which are characterized by straight lines and right angles. In non-Euclidean spaces, such as curved surfaces, the concept of orthogonality becomes more complex and cannot be described by infinitesimal small rotations.

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