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Given a matrix A, let |A| denote its determinant. Then |A||A_(rs,pq)|=|A_(r,p)||A_(s,q)|-|A_(r,q)||A_(s,p)|, (1) where A_(u,w) is the submatrix of A formed by the ...

The numbers of eigenvalues that are positive, negative, or 0 do not change under a congruence transformation. Gradshteyn and Ryzhik (2000) state it as follows: when a ...

The resultant of the vectors represented by the three radii from the center of a triangle's circumcircle to its polygon vertices is the segment extending from the ...

The study of the meaning and relationships of statements used to represent precise mathematical ideas. Symbolic logic is also called formal logic.

The symmedial circle is the circumcircle of the symmedial triangle. It has circle function l=(bc(a^4-a^2b^2-b^4-a^2c^2-b^2c^2-c^4))/(2(a^2+b^2)(a^2+c^2)(b^2+c^2)), (1) which ...

A mathematical object is said to be symmetric if it is invariant ("looks the same") under a symmetry transformation. A function, matrix, etc., is symmetric if it remains ...

A symmetric design is a block design (v, k, lambda, r, b) with the same number of blocks as points, so b=v (or, equivalently, r=k). An example of a symmetric block design is ...

A relation R on a set S is symmetric provided that for every x and y in S we have xRy iff yRx. The symmetric relations on n nodes are isomorphic with the rooted graphs on n ...

A quartic surface which is the locus of zeros of the determinant of a symmetric 4×4 matrix of linear forms. A general symmetroid has 10 ordinary double points (Jessop 1916, ...

A symmetry group is a group of symmetry-preserving operations, i.e., rotations, reflections, and inversions (Arfken 1985, p. 245).