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table of contents
-  Linear Algebra
-  Vector Analysis
-  Calculus
-  Statistics
-  Engineering
Linear Algebra

  Rotation matrix

  • Rodrigues' rotation formula
  • Euler angle

  Matrix

  • Inverse matrix
    • Inverse matrix of a 2x2 matrix
    • Inverse matrix of a 3x3 matrix
    • Inverse matrix of a 4x4 matrix
    • Gauss-Jordan elimination
  • Transpose
  • Orthogonal matrix
  • Identity matrix

  Determinant

  • Definition of Determinant
  • Properties of Determinant
  • Determinant 2x2
  • Determinant 3x3
  • Determinant 4x4
  • Determinant 5x5
  • "a matrix is invertible" $\Longleftrightarrow$ "its determinant is non-zero"

  Cofactor

  • Cofactor expansion
  • Cofactor matrix

  Diagonalization

  • How to diagonalize a 3x3 matrix

  Rank

  • How to calculate the rank of a matrix

  Others

  • Linear-independence/dependence and examples
  • Trace
  • Triangle Inequality
  • Calculator of system of linear equations
Vector Analysis
  • Norm of Cross Product = Parallelogram Area
  • Kronecker's delta
Calculus

  Integral

  • Gaussian integral
Statistics
  • Geometric Distribution
  • Variance of the exponetial Distribution
  • Expectation value of the exponential Distribution
Engineering
  • Example of Newton's method: Computing the square root of 3
  • Lagrange interporation

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