Question on definition of Span

In summary, the term "span" has multiple definitions across different fields, but it generally refers to distance or extent between two points or boundaries, time coverage, or range of influence. In mathematics, the span of a set of vectors is all possible linear combinations of those vectors. In computer science, it can refer to data type width or a specific programming language feature. "Range" refers to the entire set of values within boundaries, making "span" a subset of "range." In engineering, span is used to refer to distance between supports, points on a curve, or projectile travel distance.
  • #1
Tzar
74
0
I'm a bit confused on something elementary.
If X is a Hilbert space and A is a subset of X and is uncountable. What exactly does it mean for an element x to be in the span of A? Does it mean x can be expressed as a finite linear combination of elements from A, or can it be infinite and even possibly an uncountble linear combination?
 
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  • #2
FINITE linear combination.
 
  • #3
Thanks. I was thinking that as well but wasn't sure.
 

FAQ: Question on definition of Span

What is the definition of Span?

The term "span" has several different definitions in various fields, but in general, it refers to the distance or extent between two points or boundaries. It can also refer to the amount of time something covers or the range of influence or control of something.

What is the mathematical definition of Span?

In mathematics, the span of a set of vectors is the set of all possible linear combinations of those vectors. In other words, it is the space that can be reached by adding together any combination of those vectors with different coefficients.

How is Span used in computer science?

In computer science, the term "span" is often used to refer to the width or range of a data type. It can also refer to a specific feature in programming languages, such as the span element in HTML, which is used to identify and group a section of content.

What is the difference between Span and Range?

While both terms refer to a distance or extent, "span" typically refers to the distance between two points or boundaries, while "range" refers to the entire set of values within those boundaries. In other words, span is a subset of range.

How is Span used in engineering?

In engineering, span is often used to refer to the distance between supports in a structure, such as a bridge or building. It can also refer to the distance between two points on a curve or the distance a projectile travels through the air.

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