Concepts3
∑MathIntermediate
Matrix Rank and Linear Independence
Matrix rank is the number of pivots after Gaussian elimination and equals the dimension of both the column space and the row space.
#matrix rank#linear independence#gaussian elimination+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