Geometric description of span

  • What is a geometric description?

    Give a Geometric description of the set of points in space whose coordinates satisfy the pair of equations or inequalities. 1) z=x+1 , no restriction on y. 2) x2+y2+z2=25, x=3.
    Follow 3..

  • What is a span geometrically?

    The geometric span is largest possible distance between two points drawn from a finite set of points.
    It is therefore closely related to the generalized diameter of a closed figure..

  • What is the description of span?

    : an extent, stretch, reach, or spread between two limits: such as. a. : a limited space (as of time) especially : an individual's lifetime..

  • What is the geometric description of a subspace?

    Descriptions of subspaces include the solution set to a homogeneous system of linear equations, the subset of Euclidean space described by a system of homogeneous linear parametric equations, the span of a collection of vectors, and the null space, column space, and row space of a matrix..

  • What is the geometric description of span vectors?

    If two vectors are linearly dependent their span is the line determined by the vectors (the line made by a vector starting at the origin).
    If two vectors are linearly independent their span is the plane.
    For three linearly independent vectors the span is the entire three dimensional space..

  • What is the geometrical meaning of linear span?

    If a plane is spanned by vectors u and v, then. all possible vectors b located in this plane can. be expressed as. b = x1u + x2v where x1 and x2 are arbitrary scalars.
    We say that b is comprised of a linear combination of the vectors u and v..

  • Give a Geometric description of the set of points in space whose coordinates satisfy the pair of equations or inequalities. 1) z=x+1 , no restriction on y. 2) x2+y2+z2=25, x=3.
    Follow 3.
  • The span of a set of vectors, also called linear span, is the linear space formed by all the vectors that can be written as linear combinations of the vectors belonging to the given set.
The geometric span is largest possible distance between two points drawn from a finite set of points. It is therefore closely related to the generalized diameter of a closed figure.
The span of a collection of vectors v1, v2, , vn is just the set of all linear combinations of v1, v2, , vn. If we have one vector v the span consists of all multiples λ v. The span of one non-zero vector v is just the set of vectors parallel to this vector (the span of the zero vector is just the origin).

How do you know if a span is a 3-dimensional space?

If there is only one, then the span is a line through the origin

If there are two then it is a plane through the origin

If all are independent, then it is the 3-dimensional space

Thanks, but i did that part as mentioned

I am asking about the second part of question "geometric description of span {v1v2v3}

What is the span of a set of vectors?

The span of a set of vectors has an appealing geometric interpretation

Remember that we may think of a linear combination as a recipe for walking in Rm

We first move a prescribed amount in the direction of v1, then a prescribed amount in the direction of v2, and so on

What is the span of two vectors with the same slope?

What you end up with is the whole line y = x, which is what you get if you extend v infinitely in either direction

Note that this is determined by it's slope

So the span of two vectors with the same slope is still just the same line

Now, the span of two vectors are all of the combinations a v + b w

We will introduce a concept called span that describes the vectors b b for which there is a solution. Since we would like to think about this concept geometrically, we will consider an m × n m × n matrix A A as being composed of n n vectors in Rm; R m; that is, A =[v1 v2 … vn]. A = [ v 1 v 2 … v n].If there is only one, then the span is a line through the origin. If there are two then it is a plane through the origin. If all are independent, then it is the 3-dimensional space.

Weighted undirected graph with graph distances linearly bounded w.r.t. Euclidean distances

A geometric spanner or a texhtml mvar style=font-style:italic>t-spanner graph or a texhtml mvar style=font-style:italic>t-spanner was initially introduced as a weighted graph over a set of points as its vertices for which there is a texhtml mvar style=font-style:italic>t-path between any pair of vertices for a fixed parameter texhtml mvar style=font-style:italic>t.
A texhtml mvar style=font-style:italic>t-path is defined as a path through the graph with weight at most texhtml mvar style=font-style:italic>t times the spatial distance between its endpoints.
The parameter texhtml mvar style=font-style:italic>t is called the stretch factor or dilation factor of the spanner.

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