Matrix

• Determinant: $det(A)$

  $det(A^T) = det(A)$

• Transpose: $A^T$

• Minor: A minor-matrix $M_{ij}$ is a determinant of sub-matrix after deleting $row_i$ and $column_j$

• Cofactor: $cofactor(A) = (-1)^{i+j}\times M_{ij}$

• Adjoint: $adj(A) = cofactor(A)^T$

• Inverse:

$$ A^{-1} = \frac{adj(A)}{det(A)} $$

• Symmetric: $A^T = A$
• Skew-symmetric: $A^T = -A$
• $det(A) = \text{product of all eigenvalues of } A$

Calculus - Limits & Derivatives

Newton's method

$$ x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)} $$

Point of inflection

Given $f(x)$ is a contiguous graph, calculate $f''(x)$ and analyze the solutions.

1. Find the solution of $f''(x)$, for example $x=x_1$
2. Check if the sign change from (+) to (-) or (-) to (+) through $x_1$, so that $x_1$ is point of inflection.

Riemann Sum

$$ S=\Delta x \times \sum_{i=1}^{n}f(x^*_i) $$