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A rooted tree is a tree in which a special ("labeled") node is singled out. This node is called the "root" or (less commonly) "eve" of the tree. Rooted trees are equivalent ...

If the matrices A, X, B, and C satisfy AX-XB=C, then [I X; 0 I][A C; 0 B][I -X; 0 I]=[A 0; 0 B], where I is the identity matrix.

The divisibility test that an integer is divisible by 9 iff the sum of its digits is divisible by 9.

One of the straight lines sweeping out a ruled surface. The rulings on a ruled surface are asymptotic curves.

A scalar is a one-component quantity that is invariant under rotations of the coordinate system.

A map f:R^n|->R which assigns each x a scalar function f(x).

A diagonal matrix whose diagonal elements all contain the same scalar lambda. A scalar matrix is therefore equivalent to lambdaI, where I is the identity matrix.

Scalar multiplication refers to the multiplication of a vector by a constant s, producing a vector in the same (for s>0) or opposite (for s<0) direction but of different ...

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.

Increasing a plane figure's linear dimensions by a scale factor s increases the perimeter p^'->sp and the area A^'->s^2A.