Linear Algebra Calculators: (8) lessons

[+] Basic m x n Matrix Operations
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.

Features: Calculator | Practice Problem Generator | Watch the VideoTags: addition, matrix, multiplication, operation, scalar, subtraction
[+] Cross Product A × B
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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Examples (3): 8i-j+3k x 5i+j-9k, 6i-3j+6k * 8i+2j-9k, (8i-2j+13k)(3i+5j-k)Tags: cross product, vector
[+] Digraph Items
Given a digraph, this determines the leader, and symmetric matrix.

Features: CalculatorTags: digraph, leader, symmetric
[+] Equation of a Plane
Given three 3-dimensional points, this calculates the equation of a plane that contains those points.

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Examples (1): (2,4,6)(1,3,5)(9,8,4)Tags: equation, plane
[+] Markov Chain
Given a transition matrix and initial state vector, this runs a Markov Chain process.

Features: Calculator
[+] Matrix Properties
Given a matrix |A|, this calculates the following items if they exist:
* Determinant = det(A)
* Inverse = A-1
* Transpose = AT
* 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

Features: Calculator | Practice Problem Generator | Watch the VideoTags: adjoint, determinant, dimension, echelon, eigen, inverse, matrix, norm, polynomial, transpose
[+] Plane and Parametric Equations in R3
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


Features: Calculator | Watch the VideoTags: parametric, plane, vector
[+] Vectors
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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Examples (4): {1,2,3} + {4,5,6}, {2,4,6,8,10} + {1,3,5,7,9}, {9,8,7,6} x {4,3,2,1), {12,9,6} / {4,3,2}Tags: angle, cosine, direction, inequality, magnitude, orthogonal, orthogonal, perpendicular, product, projection, vector