## Bounds for the eigenvalues of a matrixNational Aeronautics and Space Administration; for sale by the Clearinghouse for the Federal Scientific and Technical Information, Springfield, Va., 1968 - Mathematics - 44 pages |

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_ max 4prps A*A B*B absolute value approximate arbitrary matrix arrl Bendixson Bounds by Matrix bounds for eigenvalues bounds in terms Cauchy-Schwarz inequality characteristic equation Characteristic Roots complex fields corollary A3 Corollary A6(b corresponding Define det(A diagonal matrix dominant component eigen eigenvalues of related eigenvector elementary symmetric functions exists following theorem Frobenius gives a smaller Hermitian I(A+A i=l i=l identity matrix imaginary implies that lim inclusion region inequality iteration k=l i*k k=l k*j Langley Research Center m=l m*k Math Matrix Elements matrix norm matrix of order max max max modulus nonsingular nonsingular matrix ovals of Cassini partitioned polynomial proof of theorem related matrices results of theorem scalar solutions submatrix summable matrix terms of eigenvalue theorem A3 theorem C4 Trace A2 transpose unit circle vector norm x,Ax x,Hx xi,Axi Xmax Xmin y,(diag Xi)y y,Az z,Ay