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Can unit vector have negative component?
Yes, a unit vector can have negative component since a unit vector has same magnitude and direction as a negative unit vector. Here is the general work out of the problem: Let |v| be the norm of (v1, v2). Then, the unit vector is (v1/|v|, v2/|v|). Determine the "modulus" or the norm |(v1/|v|, v2/|v|)| to get 1, which is the new norm. If we determine the norm of |(-v1/|v|, -v2/|v|)|, we still have the same norm 1.
Prove that Hilbert Space is a Metric Space?
The question doesn't make sense, or alternatively it is true by definition. A Hilbert Space is a complete inner product space - complete in the metric induced by the norm defined by the inner product over the space. In other words an inner product space is a vector space with an inner product defined on it. An inner product then defines a norm on the space, and every norm on a space induces a metric. A Hilbert Space is thus also a complete metric space, simply where the metric is induced by the inner product.
Applications of vector calculus in engineering?
Electromagnetic fields, gravitational fields and fluid flow. If you are an engineer you will come across vector calculus to handle three dimensional space.
What is null vector?
NULL VECTOR::::null vector is avector of zero magnitude and arbitrary direction the sum of a vector and its negative vector is a null vector...
When do you get a magnitude of 0 in vector?
The magnitude of a vector is 0 if the magnitude is given to be 0.The magnitude of the resultant of several vectors in n-dimensional space is 0 if and only if the components of the vectors sum to 0 in each of a sewt of n orthogonal directions.
What is Norm linear space?
A normed vector space is a pair (V, ‖·‖ ) where V is a vector space and ‖·‖ a norm on V.We often omit p or ‖·‖ and just write V for a space if it is clear from the context what (semi) norm we are using.In a more general sense, a vector norm can be taken to be any real-valued vector that satisfies these three properties. The properties 1. and 2. together imply that if and only if x = 0.A useful variation of the triangle inequality is for any vectors x and y.This also shows that a vector norm is a continuous function.
What is quasi banach spaces?
It is a vector space with a quasi norm instead of a norm. A quasi norm is a variation of a norm which follows all the norm axioms except for the triangle inequality where we have x+y< or = K(x+y)for some K>1
The length of a vector indicates the magnitude of the vector.?
Yes, the length of a vector, also known as its magnitude or norm, represents the size or extent of the vector in space. It is calculated using mathematical formulas that involve the components of the vector. A vector with greater length denotes a larger magnitude in comparison to a vector with a smaller length.
Can unit vector have negative component?
Yes, a unit vector can have negative component since a unit vector has same magnitude and direction as a negative unit vector. Here is the general work out of the problem: Let |v| be the norm of (v1, v2). Then, the unit vector is (v1/|v|, v2/|v|). Determine the "modulus" or the norm |(v1/|v|, v2/|v|)| to get 1, which is the new norm. If we determine the norm of |(-v1/|v|, -v2/|v|)|, we still have the same norm 1.
Prove that Hilbert Space is a Metric Space?
The question doesn't make sense, or alternatively it is true by definition. A Hilbert Space is a complete inner product space - complete in the metric induced by the norm defined by the inner product over the space. In other words an inner product space is a vector space with an inner product defined on it. An inner product then defines a norm on the space, and every norm on a space induces a metric. A Hilbert Space is thus also a complete metric space, simply where the metric is induced by the inner product.
Is it possible to define position 4-vector of finite norm in curved space time?
Yes, very much possible it is. It is actually very simplistic.
How do you compute norm on matlab?
using the function norm(A,x) where A is the matrix/vector that you have to compute the norm for and x can be 1,2,inf, or 'fro' to compute the 1-norm, 2-norm, infinite-norm and frobenius norm respectively.
What is an under vector room?
There does not seem to be an under vector room, but there is vector space. Vector space is a structure that is formed by a collection of vectors. This is a term in mathematics.
What is relationship between vector space and vector subspace?
Vector spaces can be formed of vector subspaces.
Direction of vector in space is specified by?
It is an integral part of the vector and so is specified by the vector.
What is an affine space?
An affine space is a vector space with no origin.
What is the difference between zero and vector zero?
The zero vector occurs in any dimensional space and acts as the vector additive identity element. It in one dimensional space it can be <0>, and in two dimensional space it would be<0,0>, and in n- dimensional space it would be <0,0,0,0,0,....n of these> The number 0 is a scalar. It is the additive identity for scalars. The zero vector has length zero. Scalars don't really have length. ( they can represent length of course, such as the norm of a vector) We can look at the distance from the origin, but then aren't we thinking of them as vectors? So the zero vector, even <0>, tells us something about direction since it is a vector and the zero scalar does not. Now I think and example will help. Add the vectors <2,2> and <-2,-2> and you have the zero vector. That is because we are adding two vectors of the same magnitude that point in opposite direction. The zero vector and be considered to point in any direction. So in summary we have to state the obvious, the zero vector is a vector and the number zero is a scalar.
