0
Add your answer:
Earn +20 pts
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 the relationship between the infinity norm and the 2 norm in a vector space, and how can one be less than the other?
In a vector space, the infinity norm and the 2 norm are different ways to measure the size of a vector. The infinity norm is the maximum absolute value of any component in the vector, while the 2 norm is the square root of the sum of the squares of all the components. The infinity norm can be less than the 2 norm when the vector has a few very large components that dominate the sum of squares in the 2 norm calculation.
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 the significance of the discrete L2 norm in mathematical analysis and how does it differ from other norms in the context of numerical computations?
The discrete L2 norm is important in mathematical analysis because it measures the magnitude of a vector in a discrete space. It differs from other norms in numerical computations because it considers the square of each component of the vector, making it useful for minimizing errors and optimizing algorithms.
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.
