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Browse College Linear Algebra

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Tensor Calculus [03/06/1998]
Scalars, vectors, and tensors, and their components.

Two Methods for Finding an Optimum Point in 3D Space [10/24/2005]
I have more than two lines in space which should intersect but don't because of measuring errors. How can I find the optimum intersection point that minimizes the error?

Understanding Vector Spaces [03/14/2001]
What does a vector space in R^n mean? How can I prove that a list of numbers is a vector space?

Unit Vectors [07/02/2002]
Find the two unit vectors that are collinear with each of the following vectors. (a) vector A = (3, -5). I don't understand--is a unit vector only ever equal to 1?

Using an Augmented Matrix [11/21/1999]
Solve the set of simultaneous equations x+3y+z=3, x+5y+5z=1 and 2x+6y+ 3z=8 using an augmented matrix?

Vandermonde Determinant [02/11/2003]
Compute the n x n determinant...

Vector Algebra: Finding the Intersection Point [04/23/2003]
If I have two lines in three dimensions that I know intersect at some point, how do I work out what that point is? Both lines are defined by two points on each line.

Vectors and Orientation [05/29/2003]
I am trying to write a game involving spaceships, and I have been having trouble finding relative positions.

Vectors and the Volume of Parallelepipeds [03/08/2003]
Explain the derivation of the formula V = |a.(b x c)| (the volume of a parallelepiped is equal to the magnitude of the scalar triple product of the vectors that determine the parallelepiped; where a, b, and c are those vectors).

Vector Space Dimensions [12/09/1997]
Why does C^2 considered as a vector space over the complex numbers have dimension 2, but as a vector space over the real numbers have dimension 4?

Volume of a Tetrahedron [01/23/2002]
The volume of a tetrahedron is one-third the distance from a vertex to the opposite face, times the area of that face. Find a formula for the volume of a tetrahedron in terms of the coordinates of its vertices P, Q, R, and S.

Why Transpose a Matrix? [03/23/2008]
Why is a transpose of a matrix needed? I know how to transpose a matrix, I just don't know what purpose it serves. I have read through my text as well as consulted online help without finding any answers.

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