Permutation Matrix
A Matrix 
obtained by permuting the 
th and 
th rows of the Identity Matrix with 
.Every row and column therefore contain precisely a single 1, and every permutation corresponds to a unique permutationmatrix. The matrix is nonsingular, so the Determinant is always Nonzero. It satisfies
where I is the Identity Matrix. Applying to another Matrix,
gives A with theth and th rows interchanged, and 
gives A with the th and th columns interchanged.Interpreting the 1s in an 
permutation matrix as Rooks gives an allowable configuration ofnonattacking Rooks on an Chessboard.
- Stellated Tetrahedron
- Stellated Truncated Hexahedron
- Stellation
- Stem-and-Leaf Diagram
- Step
- Step Function
- Step Polynomial
- Steradian
- Stereogram
- Stereographic Projection
- Stereology
- Stern-Brocot Tree
- Stevedore's Knot
- Stewart's Theorem
- Stickelberger Relation
- Stick Number
- Stiefel Manifold
- Stiefel-Whitney Class
- Stiefel-Whitney Number
- Stieltjes Constants
- Stieltjes Integral
- Stieltjes' Theorem
- Stieltjes-Wigert Polynomial
- Stirling Cycle Number
- Stirling Number of the First Kind