First, I don't understand what you mean by a vector "occupying" 7 dimensions. A vector is, pretty much by definition, a one dimensional object, no matter what the dimension of the underlying space. Perhaps that is your misunderstanding. You may be think of the vector as "taking up" the entire space. That is not true in 7 dimensions any more than it is true in 3 dimensions. You are talking about vector s in 7 dimensions, not "occupying" 7 dimensions.robertjford80 said:Apparently you can calculate the angle between two vectors even when they occupy say 7 dimensions. I have trouble believing that. To me if a vector occupies 7 dimensions than it is incommensurable with another vector occupying 7 dimensions.
No, the calculation of the angle between two vectors in 7-dimensional space requires a different method due to the increased number of dimensions. In 2 or 3-dimensional space, the angle can be calculated using the dot product and inverse cosine function. However, in 7-dimensional space, the dot product is not defined and a different approach must be used.
The mathematical formula for finding the angle between two 7-dimensional vectors involves using the concept of inner product spaces and the concept of norms. It is a more complex formula that cannot be easily simplified or explained without a deep understanding of advanced mathematics.
No, the angle between two vectors in any number of dimensions cannot exceed 180 degrees. This is because the angle between two vectors is defined as the smallest angle between them, and an angle greater than 180 degrees would not be the smallest angle.
Yes, there are many practical applications for calculating the angle between two 7-dimensional vectors in fields such as physics, engineering, and computer science. For example, in physics, the angle between two vectors can help determine the direction and magnitude of a force acting on an object.
No, it is not possible to visualize the angle between two 7-dimensional vectors in the same way that we can visualize it in 2 or 3-dimensional space. This is because our brains are not equipped to visualize objects in more than 3 dimensions. However, there are mathematical techniques that can be used to represent and understand higher-dimensional spaces.