Concepts5
∑MathIntermediate
Linear Diophantine Equations
A linear Diophantine equation ax + by = c has integer solutions if and only if gcd(a, b) divides c.
#linear diophantine#extended euclidean algorithm#gcd+12
⚙️AlgorithmIntermediate
Orientation and CCW
Orientation (CCW test) tells whether three points make a left turn, right turn, or are collinear by using the sign of a 2D cross product.
#orientation#ccw#cross product+12
∑MathIntermediate
Gaussian Elimination
Gaussian elimination is a systematic way to solve linear equations by cleaning a matrix into an upper-triangular form using row swaps, scaling, and adding multiples of rows.
#gaussian elimination#partial pivoting#row echelon form+12
∑MathIntermediate
Determinant
The determinant of a square matrix measures how a linear transformation scales volume and whether it flips orientation.
#determinant#gaussian elimination#lu decomposition+12
∑MathIntermediate
Matrix Inverse
A matrix inverse undoes the effect of a linear transformation, just like dividing by a number undoes multiplication.
#matrix inverse#gauss-jordan#lu factorization+12