If X is an m x m

symmetric matrix, and R is an m x m symmetric positive definite matrix, then the eigenvalues of RX are same as those of [R.

Mathematically, we have a discretized differential operator embodied in a real

symmetric matrix pair, ([A.

The analyst is reminded that any matrix can be reduced to the sum of a

symmetric matrix and a skew-

symmetric matrix (Tobler, 1976).

By a

symmetric matrix game, we mean its payoff matrix is symmetric around the diagonals, while by an anti-diagonally

symmetric matrix game, we mean the payoff matrix is symmetric around the anti-diagonals.

A) denote the number of positive eigenvalues of a given

symmetric matrix A, and let [e.

For any vectors or matrices z, y with appropriate dimensions and any positive

symmetric matrix P [is greater than] 0, the following inequalities are satisfied:

In two pages, Rubinstein crisply presents the definition and the corresponding Nash-type equilibrium, mentions the limiting behavior (for EU max and also the opposite direction) in a simple 2 x 2

symmetric matrix game, and goes off in a different direction in the next subsection.

Since most FEA strives for a

symmetric matrix, the invention of the actuator elements necessitated that a new solver be developed.

represents the elements below the main diagonal of a

symmetric matrix.

Computation in linear time of the Frobenius norm for a proper represented (in the G-d, Givens vector representation) semiseparable

symmetric matrix can be found in [11].

Thus, x satisfies the following complex linear equation with

symmetric matrix A

Since A is a real

symmetric matrix, its eigenvalues are real number.