Concepts6

DP with Probability

DP with probability models how chance flows between states over time by repeatedly redistributing mass according to transition probabilities.

#markov chain#probability dp#absorbing state+12

⚙️AlgorithmAdvanced

DP with Expected Value

Dynamic programming with expected value solves problems where each state transitions randomly and we seek the expected cost, time, or steps to reach a goal.

#expected value dp#linearity of expectation#indicator variables+11

∑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

∑MathAdvanced

Gaussian Elimination over GF(2)

Gaussian elimination over GF(2) is ordinary Gaussian elimination where addition and subtraction are XOR and multiplication is AND.

#gaussian elimination#gf(2)#xor basis+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