TOPICS
This page:
linear algebra
Search
Dr. Math
See also the
Internet Library:
linear algebra
COLLEGE
Algorithms
Analysis
Algebra
linear algebra
modern algebra
Calculus
Definitions
Discrete Math
Exponents
Geometry
Euclidean/plane
conic sections/
circles
constructions
coordinate plane
triangles/polygons
higherdimensional
polyhedra
nonEuclidean
Imaginary/Complex
Numbers
Logic/Set Theory
Number Theory
Physics
Probability
Statistics
Trigonometry

Browse College Linear Algebra
Stars indicate particularly interesting answers or
good places to begin browsing.
 Eigenvectors and Matrices [09/01/1997]

Can you please give me an example of a practical use of eigenvalues and
eigenvectors?
 Eigenvectors of a Covariance Matrix [07/04/2004]

Why do the eigenvectors of a covariance matrix point in the direction
of highest variance of the initial data set?
 Eliminating Multiple Radicals in an Equation [02/23/2006]

How can I solve equations containing different radicals, such as
cuberoot(y) + fourthroot(x) = 1?
 Equation for Angle Formed by Two Vectors [05/31/2000]

Do I need to find the vector equation of OP and OQ, or of PO and OQ, when
finding the angle POQ using the formula cos(theta)=a.b/ab?
 Equation of a Line in Three or More Dimensions [05/18/2000]

Can the equation y = mx + b be used to define a line in three dimensions?
What about four or more dimensions?
 Expansion by Minors [10/26/1999]

How do you evaluate the determinant of a 3x3 matrix using expansion by
minors?
 Explaining the Determinant [11/16/1997]

I am trying to understand what the determinant of a matrix actually is.
 Explaining the Dot Product [04/05/1998]

Exactly what does the dot product represent?
 Explanation of General Solution to Difference Equations [02/08/2006]

I know that the general solution to a difference equation like y(n) =
Ay(n1) + By(n2) is given by y(n) = as^n + bs^n when y is in the form
s^t. But I don't really know why that's the case. Can you explain
where that comes from?
 Finding Area Using a Determinant [05/25/2007]

Given two vectors defining a parallelogram, the area can be found
using the determinant of the 2x2 matrix representing those vectors. I
can't figure out why that works. Can you explain it?
 Finding a Transformation Matrix [12/29/2003]

Vectors a1(4,2,1), a2(5,3,2), a3(3,2,1) and b1(1,4,0), b2(4,3,1), b3
(5,7,3) are two bases for V3. What is the transformation matrix
from first to second base?
 Finding Eigenvalues and Eigenvectors [06/27/2007]

In a 3x3 square matrix, how would you find the eigenvalues and
eigenvectors?
 Finding Eigenvectors from Eigenvalues [08/24/2005]

Given a 3 x 3 matrix, find the eigenvalues and the corresponding
eigenvectors.
 Finding Parametric Equations for a Line [05/24/2000]

How can I find the parametric equations for the line of intersection of,
and the angle between, two planes given by x2y+z=0 and 2x+3y2z= 0?
 Finding the Area of an Irregular Polygon in 3D [02/04/2009]

Given the coordinates of eight points in threedimensional space, with
no known angles, how can I find the area of the polygon they define?
 Finding the Jordan Canonical Form [04/29/1998]

I need help in finding the Jordan Canonical Form of a matrix.
 Finding Two Orthogonal Vectors in R3 [12/15/2003]

I'm supposed to find two nonzero vectors in R3 that are orthogonal,
but I'm pretty confused about the whole idea. Can you explain it to me?
 Fitting Equation to Data with Regression Techniques [04/20/2007]

I have a set of data and I'm trying to find a bestfit equation. I've
used linear regression with little success, and I don't know much
about how to do other nonlinear regressions. Can you get me started?
 General Form of a Line [5/19/1996]

What is the equation is for the general form of a line in three
dimensions? in n dimensions? What would be a test for collinearity of
points in three dimensions? in n dimensions?
 Gradient and Maximum Increase of a Function [07/19/2005]

Why does the gradient point in the direction of the maximum increase
of a function? Several resources make the statement, but no one
explains it. Can the dot product be used to justify it?
 Intersecting Vectors and the Dot Product [04/24/1998]

Each of the following geometrical theorems can be proved with vectors,
using the dot product...
 Intersection of Ellipsoid and Plane [05/04/2007]

I need to find the general equation of the ellipse resulting from the
intersection of an ellipsoid and a plane. When I solve the system of
two equations, I wind up with an xy term and need to know how to
eliminate that from the final equation of the ellipse.
 The Intersection of Two Subspaces [10/11/1998]

If w1 and w2 are subspaces of the vector space V, how can I prove that
their intersection is also a subspace of V?
 Intersection Point of Two Lines [07/22/2003]

I want to find the intersection point of two lines (in 3D) defined
by a point on each line and their direction vectors V1 and V2.
 Inverse of a 3x3 Matrix [04/25/2001]

How can I obtain the inverse of a 3x3 matrix?
 Inverse of a Matrix [12/05/1997]

I need an algorithm to compute the inverse of a matrix.
 Invertible Matrices [12/07/2001]

Show that if A and B are nxn invertible matrices, then A^(1)=(A+B)^(
1)+(A+AB^(1)A)^(1).
 Irreducible Polynomials [06/06/2001]

If provided with an irreducible polynomial, how can you prove that it is
indeed irreducible? E.g. the polynomial x^8+x^4+x^3+x+1 (Hex: x'11B').
 Linear Algebra and Proving a Subspace [02/04/2004]

(a) The set Sm = {(2a,b  a,b + a,b) : a,b are real numbers. Under
the operations of matrix addition and multiplication, prove that this
is a subspace of M22. (b) Find a basis for this subspace and give the
dimension of the subspace.
 Linear Algebra  Definition of Orthonormal [10/28/1997]

Show that the transition matrix P from one orthonormal basis to another
is unitary, that is, P*P = I.
 Line of Best Fit For Points in Three Dimensional Space [11/22/2005]

How can I find the line that most closely fits a set of points in 3D
space, like the least squares line does in two dimensions?
 Matrix Inversion by the CayleyHamilton Theorem [02/27/1998]

What is the CayleyHamilton Theorem is and how it is used to find the
inverse of a matrix?
 Matrix Multiplication [09/04/1997]

I am doing a project in Algebra 2 and must research matrix
multiplication.
 Matrix Pattern Tells Solution Set? [9/4/1996]

Is there a pattern for reduced rowechelon form matrices that can
differentiate whether the solution set has no, one, or infinitely many
solutions?
 Matrix Rank [09/29/2001]

I want to find the rank of a matrix, but I don't know how to compute
rank.
 Matrix Representation of Complex Numbers [11/15/2000]

How can I find matrices A and B such that (A+B)^1 = A^1 + B^1?
 Matrix Theory [06/06/2001]

I would like to know how to calculate the Jordan canonical form of the
matrix with columns: [(1 4 2 3 8),(0 1 1 1 2),(1 3 0 3  7),(1
2 1 4 5),(0 1 1 1 4)].
 Maximum Difference, Longitude and Latitude [04/10/2001]

Find the maximum longitude and latitude difference between two points on
Earth 1000 kilometers apart.
 Minimum Matrix Multiplication [02/16/2003]

Find a way to multiply n matrices using a minimum number of
multiplications of the entities.
 Multiplicative Inverse in Finite Field GF(2^8) [02/23/2005]

Is the multiplicative inverse of a 4x4 matrix in GF(2^8) the same as
the inverse of any 4x4 matrix?
Page: [<prev]
1
2
3
4
[next>]
