## Linear Algebra Calculators: (8) lessons

Basic m x n Matrix Operations
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.
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Cross Product
Free Cross Product Calculator - Given two vectors A and B in R3, this calculates the cross product A × B as well as determine if the two vectors are parallel
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Digraph Items
Free Digraph Items Calculator - Given a digraph, this determines the leader, and symmetric matrix.
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Equation of a Plane
Free Equation of a Plane Calculator - Given three 3-dimensional points, this calculates the equation of a plane that contains those points.
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Markov Chain
Free Markov Chain Calculator - Given a transition matrix and initial state vector, this runs a Markov Chain process.
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Matrix Properties
Free Matrix Properties Calculator - Given a matrix |A|, this calculates the following items if they exist:
* Determinant = det(A)
* Inverse = A-1
* Transpose = AT
* 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
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Plane and Parametric Equations in R3
Free Plane and Parametric Equations in R3 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
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Vectors
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, projBA and and the vector component of A orthogonal to B → A - projBA
Also calculates the horizontal component and vertical component of a 2-D vector.
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