# real matrix

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Related to real matrix: symmetric matrix, Real numbers
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 Noun 1 real matrix - a matrix whose elements are all real numbersmatrix - (mathematics) a rectangular array of quantities or expressions set out by rows and columns; treated as a single element and manipulated according to rules
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Input: real matrix A, two real vectors v, w such that w*v [not equal to] 0.
Let A [member of] [R.sup.nxn] be a real matrix and 1 [less than or equal to] [alpha] < 2.
Suppose that E = diag(F, F, ..., F) is an n x n nonsingular idempotent matrix and that F is a real matrix. Then by Lemma 2 we can find that F is an (n/k) x (n/k) real nonsingular idempotent matrix.
It has been proven that this real matrix is symmetrical, and hence, both matrix decomposition and spectral search can be implemented with real-valued computation.
The score function is basically a real matrix in classical sense derived from two or more value matrices.
Lemma 1  : Let A be any real matrix defined by A [member of] [A.sub.1] := {A = ([[alpha].sub.ij]) : [A.bar] [less than or equal to] A [less than or equal to] [bar.A], i.e., [[a.bar].sub.ij] [less than or equal to] [a.sub.ij] [less than or equal to] [[bar.a].sub.ij], i,j = 1,2,...,n}.
Written A [greater than or equal to] 0 if each entry of a real matrix (or vector) A is nonnegative.
and [K.sub.i] [member of] [R.sup.mxn] is a real matrix to be designed and [G.sub.i] [member of] [R.sup.mxn] is a constant matrix satisfying [G.sub.i][B.sub.i] being nonsingular.

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