Vector valued and scalar valued functions

Thread starter Odyssey
Start date Oct 10, 2004
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In summary, vector valued functions map a single input to a vector output, while scalar valued functions map a single input to a single scalar value. They are commonly used in physics to represent physical quantities with both magnitude and direction, as well as quantities with only magnitude. A vector valued function can have a scalar input, and an example of a real-world application is in computer graphics. Vector valued functions can be seen as a generalization of scalar valued functions.

Oct 10, 2004

Odyssey

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.

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Oct 10, 2004

arildno

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The output of a "scalar function" is a scalar, that is just a number.

The output of a "vector function" is a vector.

Oct 10, 2004

Odyssey

thanks arildno!

1. What is the difference between a vector valued function and a scalar valued function?

A vector valued function maps a single input to a vector output, while a scalar valued function maps a single input to a single scalar value.

2. How are vector valued functions and scalar valued functions used in physics?

Vector valued functions are commonly used to represent physical quantities with both magnitude and direction, such as velocity and force. Scalar valued functions are used to represent quantities with only magnitude, such as temperature or mass.

3. Can a vector valued function have a scalar input?

Yes, a vector valued function can have a scalar input. For example, a vector valued function representing the displacement of an object can have a scalar input of time.

4. What is an example of a real-world application of a vector valued function?

An example of a real-world application of a vector valued function is in computer graphics, where vector valued functions are used to represent the position and orientation of objects in 3D space.

5. How are vector valued functions and scalar valued functions related?

Vector valued functions can be seen as a generalization of scalar valued functions, as they encompass scalar valued functions as a special case where the output is a vector with only one component.