Vector valued and scalar valued functions

Click For Summary
A scalar valued function produces a single numerical output, representing a quantity without direction. In contrast, a vector valued function generates an output that is a vector, which includes both magnitude and direction. The geometric interpretation of scalar functions relates to points on a number line, while vector functions can be visualized as arrows in space. Understanding these definitions is crucial for applications in physics and engineering. Clarifying these concepts enhances comprehension of mathematical functions in various contexts.
Odyssey
Messages
84
Reaction score
0
Hi what is the definition and meaning (geometric) of a vector valued and scalar valued function?

I read the definition in the textbook but I didn't quite get it.

Thank you.
 
Mathematics news on Phys.org
The output of a "scalar function" is a scalar, that is just a number.

The output of a "vector function" is a vector.
 
thanks arildno!
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

Undergrad Label propagation equation: what are the terms?
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad How to prove that a scalar potential exists if the curl of the vector point function is zero?
  • · Replies 2 ·
Replies
2
Views
1K
Insights Why Vector Spaces Explain The World: A Historical Perspective
  • · Replies 0 ·
Replies
0
Views
8K
High School Notation for a "scalar absolute field"?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Magnitude of the gradient of a constant scalar field
  • · Replies 16 ·
Replies
16
Views
4K
Undergrad What are the applications of inverses of vector functions?
  • · Replies 17 ·
Replies
17
Views
3K
Undergrad Why are scalars and dual vectors 0- and 1-forms?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad How to do algebra on the Kitaev toric code grid?
  • · Replies 18 ·
Replies
18
Views
2K
High School When are two vectors collinear and coplanar?
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Theory of "fields" in the sense of fields in physics?
  • · Replies 18 ·
Replies
18
Views
2K