# Mathematics

Mathematics lessons and notes

**Algebra**

- The zero product law
- The identity principle of polynomials
- Division by Zero
- Undefined operations in mathematics

**Sets**

**Geometry**

**Trigonometry**

**Matrices**

- Matrices
- Row-column multiplication
- Element-wise product (Hadamard product)
- Determinant
- Rank
- Trace
- Minors of a matrix
- Symmetric matrix
- Opposite matrix
- Identity matrix
- Zero matrix
- Transpose of a matrix
- Square matrices
- Cofactor Matrix
- Adjugate Matrices
- Inverse Matrices

**Vectors**

- Vectors
- Scalar and vector quantities
- Equal vectors
- Vector operations
- Vector addition
- Parallelogram method
- Head-to-tail method
- Opposite vector
- Vector subtraction
- Vector multiplication
- Scalar multiplication of a vector by a constant factor
- Dot product (scalar product or inner product)
- Cross product
- Outer product
- Element-wise product (Hadamard product)
- Cartesian decomposition of a vector
- Calculating the angle between two vectors
- Length of the vector (magnitude)

**Calculus**

**Complex numbers**

- Complex numbers
- Complex plane (or Gauss plane)
- Imaginary unit ("i" or "j")
- Magnitude (modulus) of a complex number
- Argument of a complex number
- Conjugate of a complex number
- Addition complex numbers
- Subtracting complex numbers
- Multiplication
- Division
- Complex numbers in trigonometric form
- Complex numbers in exponential form

**Numerical calculation**

- Numerical calculation