Vector-valued function

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A vector-valued function is a mathematical function that maps real numbers onto vectors. Vector-valued functions can be defined as:

• [\mathbf(t)=f(t)\mathbf}+g(t)\mathbf}] or
• [\mathbf(t)=f(t)\mathbf}+g(t)\mathbf}+h(t)\mathbf}]

where f(t), g(t) and h(t) are functions of the parameter t and i, j and k are unit vectors. Vector functions can also be referred to in a different notation:

• [\mathbf(t)=\langle f(t), g(t)\rangle] or
• [\mathbf(t)=\langle f(t), g(t), h(t)\rangle]

Properties

The domain of a vector-valued function is the intersection of the domain of the functions f, g and h.

See also

• Position vector
• Bochner integral

External links

• [Vector-valued functions and their properties (from Lake Tahoe Community College)]
• , [Vector Function] at MathWorld.
  • [Everything2 article]
  • [3 Dimensional vector-valued functions (from East Tennessee State University)]

   

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  All text is available under the terms of the GNU Free Documentation License See Wikipedia Copyrights for details.

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