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The permanent of an n×n integer matrix with all entries either 0 or 1 is 0 iff the matrix contains an r×s submatrix of 0s with r+s=n+1. This result follows from the ...

Two matrices A and B are said to be equal iff a_(ij)=b_(ij) (1) for all i,j. Therefore, [1 2; 3 4]=[1 2; 3 4], (2) while [1 2; 3 4]!=[0 2; 3 4]. (3)

A conservative vector field (for which the curl del xF=0) may be assigned a scalar potential where int_CF·ds is a line integral.

The biharmonic operator, also known as the bilaplacian, is the differential operator defined by del ^4=(del ^2)^2, where del ^2 is the Laplacian. In n-dimensional space, del ...

An m×1 matrix [a_(11); a_(21); |; a_(m1)].

A vector whose elements are complex numbers.

An orthogonal projection of a cross onto a three-dimensional subspace. It is said to be normalized if the cross vectors are all of unit length.

A flow line for a map on a vector field F is a path sigma(t) such that sigma^'(t)=F(sigma(t)).

The vectors +/-a_1, ..., +/-a_n in a three-space form a normalized eutactic star iff Tx=x for all x in the three-space.

A vector field v for which the curl vanishes, del xv=0.