Free Basic m x n Matrix Operations Calculator - Given 2 matrices |A| and |B|, this performs the following basic matrix operations

* Matrix Addition |A| + |B|

* Matrix Subtraction |A| - |B|

* Matrix Multiplication |A| x |B|

* Scalar multiplication rA where r is a constant.

Free Cross Product Calculator - Given two vectors A and B in R^{3}, this calculates the cross product A × B as well as determine if the two vectors are parallel

Free Digraph Items Calculator - Given a digraph, this determines the leader, and symmetric matrix.

Free Equation of a Plane Calculator - Given three 3-dimensional points, this calculates the equation of a plane that contains those points.

Free Markov Chain Calculator - Given a transition matrix and initial state vector, this runs a Markov Chain process.

Free Matrix Properties Calculator - Given a matrix |A|, this calculates the following items if they exist:

* Determinant = det(A)

* Inverse = A^{-1}

* Transpose = A^{T}

* Adjoint = adj(A)

* Eigen equation (characteristic polynomial) = det|λI - A|

* Trace = tr(A)

* Gauss-Jordan Elimination using Row Echelon and Reduced Row Echelon Form

* Dimensions of |A| m x n

* Order of a matrix

* Euclidean Norm ||A||

* Magic Sum if it exists

* Determines if |A| is an Exchange Matrix

Free Plane and Parametric Equations in R^{3} Calculator - Given a vector A and a point (x,y,z), this will calculate the following items:

1) Plane Equation passing through (x,y,z) perpendicular to A

2) Parametric Equations of the Line L passing through the point (x,y,z) parallel to A

Free Vectors Calculator - Given 2 vectors A and B, this calculates:

* Length (magnitude) of A = ||A||

* Length (magnitude) of B = ||B||

* Sum of A and B = A + B (addition)

* Difference of A and B = A - B (subtraction)

* Dot Product of vectors A and B = A x B

A ÷ B (division)

* Distance between A and B = AB

* Angle between A and B = θ

* Unit Vector U of A.

* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).

* Cauchy-Schwarz Inequality

* The orthogonal projection of A on to B, proj_{B}A and and the vector component of A orthogonal to B → A - proj_{B}A

Also calculates the horizontal component and vertical component of a 2-D vector.