- #1

Warlord_

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Could someone please help me to understand where the second and the third equalities came from?

Thanks,

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- Thread starter Warlord_
- Start date

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.

- #1

Warlord_

- 2

- 0

Could someone please help me to understand where the second and the third equalities came from?

Thanks,

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- #2

DEvens

Education Advisor

Gold Member

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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.

- #3

Warlord_

- 2

- 0

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

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.

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.

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.

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.

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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