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
The analyst is reminded that any matrix can be reduced to the sum of a symmetric matrix
and a skew-symmetric matrix
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 .
Thus, x satisfies the following complex linear equation with symmetric matrix
Since A is a real symmetric matrix
, its eigenvalues are real number.