a matrix that already did half its homework — everything below or above the diagonal is zero.
means a square matrix where all entries above (upper) or below (lower) the main diagonal are zero, making it dramatically easier to solve.
from grew out of gaussian elimination — the systematic row-reduction method carl friedrich gauss formalized in the early 1800s, which naturally produces this staircase-of-zeros shape when solving linear systems.
lu decomposition — splits any matrix into lower and upper triangular factors
cholesky factorization — used in finance to simulate correlated random variables fast
pascal's triangle matrix — binomial coefficients arranged as a lower triangular matrix
schur decomposition — reduces any matrix to triangular form via unitary transform