Intermediate · 15 minYou are hereRead
Diagonal matrices
A matrix that is zero off its diagonal needs only n numbers. A get function supplies the zeros, set refuses anything else off the diagonal, and a product with a vector takes n steps.
Matrices and polynomials
Special matrices
Lessons on this topic
Intermediate · 20 minYou are hereRead
Triangular and symmetric matrices
A triangular matrix fits in n(n + 1)/2 cells, with a formula that maps each entry to its place, and a symmetric matrix is stored as one of its triangles.
Intermediate · 20 minYou are hereRead
Tridiagonal and banded matrices
A matrix whose non-zeros lie on a few central diagonals is stored diagonal by diagonal: 3n − 2 cells for a tridiagonal one, and a system with it is solved in about 8n steps.
Intermediate · 20 minYou are hereRead
Toeplitz matrices
A matrix that is constant along every diagonal is fixed by its first row and first column, 2n − 1 numbers for n × n, and filtering a signal is multiplying by one.
Intermediate · 25 minYou are hereRead
Sparse matrices in arrays
A matrix that is almost all zeros is stored as its non-zero entries only, as (row, column, value) triples or in compressed rows (CSR), and processed by touching only those.
Intermediate · 20 minYou are hereRead
Sparse matrices as linked lists
An array of row heads, each with a sorted chain of (column, value) nodes, lets non-zeros be inserted, changed and removed without shifting anything.
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