vector field

USAGE SUMMARY

The phrase "vector field" is correct and usable in written English.
It is used to describe an area in which each point is assigned a vector, or a set of values that indicate how a force is applied in a particular direction. For example, you can say "The wind speed and direction of a large area can be described using a vector field."

✓ Grammatically correct

Academia

Science

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

We have this vector field.

Massachusetts Institute of Technology

I have my vector field.

Massachusetts Institute of Technology

They are trajectories of the vector field.

Massachusetts Institute of Technology

A line integral of this vector field.

Massachusetts Institute of Technology

So, in fact, it's a vector field.

Massachusetts Institute of Technology

So, this vector field is not conservative.

Massachusetts Institute of Technology

It is proportional to this vector field.

Massachusetts Institute of Technology

devices that monitor a scalar or vector field.

University of California, Berkeley

Let's say that I give you this vector field.

Massachusetts Institute of Technology

So, remember, our vector field was y, x.

Massachusetts Institute of Technology

Added caching of polarization basis vector field Fourier transform matrices.

Stanford University

Expert writing Tips

Best practice

When describing physical phenomena, clearly define what the "vector field" represents (e.g., velocity, force, electromagnetic field) to ensure clarity and precision.

Common error

Avoid using "vector field" when a scalar field is more appropriate. A scalar field assigns a scalar value (magnitude only) to each point, while a "vector field" assigns a vector (magnitude and direction).

Linguistic Context

The phrase "vector field" functions as a noun phrase, typically serving as the subject or object in a sentence. It refers to a specific mathematical concept where each point in space is assigned a vector. Ludwig AI confirms that this phrase is correct and usable in written English.

Expression frequency: Very common

Frequent in

Academia

50%

Science

40%

News & Media

10%

Less common in

Formal & Business

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

The term "vector field" is a well-established and frequently used noun phrase in academic and scientific contexts. According to Ludwig AI, it is grammatically correct and describes a mathematical concept where a vector is assigned to each point in space. The term is most commonly found in academia and science, as evidenced by the source analysis. When writing about physical phenomena involving direction and magnitude, using "vector field" can provide a precise and technical description. Remember to avoid confusing it with scalar fields, which only assign a magnitude.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

force field

This alternative shifts the focus to fields representing forces, which is a common application of vector fields.

gradient field

This term specifies a vector field derived from the gradient of a scalar function.

velocity field

This alternative highlights vector fields representing velocities, especially in fluid dynamics.

directional field

This term emphasizes the directional aspect of the field, focusing on the orientation of vectors.

electromagnetic field

This refers to a specific type of vector field describing electromagnetic forces.

magnetic field

This term specifies a vector field representing magnetic forces.

electric field

This term specifies a vector field representing electric forces.

tensor field

This alternative represents a generalization of vector fields, using tensors instead of vectors.

mathematical field

This alternative broadens the concept to any field defined mathematically.

spatial vector distribution

This alternative describes how vectors are distributed throughout space.

FAQs

How can I describe a "vector field" in simpler terms?

You can describe a "vector field" as a map that assigns a vector to each point in space, indicating direction and magnitude, such as wind velocity at different locations.

In what contexts is the term "vector field" commonly used?

The term "vector field" is commonly used in physics, engineering, and mathematics to represent phenomena like fluid flow, gravitational forces, and electromagnetic fields.

What's the difference between a "vector field" and a scalar field?

A "vector field" assigns a vector (magnitude and direction) to each point in space, while a scalar field assigns only a scalar value (magnitude) to each point. Temperature distribution is an example of a scalar field.

How do I determine if a "vector field" is conservative?

A "vector field" is conservative if its curl is zero or if it is the gradient of a scalar potential function. This means the line integral of the field is path-independent.