## Matrix-Computer Methods in Engineering |

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### Contents

BASIC DEFINITIONS DETERMINANTS AND LINEAR ALGEBRAIC | 1 |

MATRIX ALGEBRA SIMULTANEOUS EQUATIONS | 22 |

EIGENVALUES EIGENVECTORS AND QUADRATIC FORMS | 55 |

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above absolute values adjoint matrix algebra angular frequency augmented matrix band-pass filter BASIC programming language calculated capacitance capacitor Cayley-Hamilton theorem Chapter characteristic equation characteristic impedance characteristic polynomial characteristic value characteristic vector circuit coefficients cofactor column matrix complex conjugate computer program constants corresponding cosh Cramer's rule degrees of freedom denote determinant diagonal diagonal matrix digital computer discussed displacements dynamical matrix dynamical system eigenvalues eigenvector equation electric circuit electromotive force Elementary Matrices energy equa equal equations of motion Euler method example exponential function Fast Fourier Transform Figure flexibility matrix FORTRAN Fourier series Fourier transform free body diagram frequency function Gauss-Seidel method given Gram determinant high-pass filter homogeneous polynomial However integral equation internal forces inverse inverse dynamical inverse matrix iteration method ITERATION NUMBER kinetic energy Kirchhoff's current law Laplace transform linear Linear Algebra linear differential equations linear equations linear transformation linearly independent loop currents low-pass filter matrix algebra matrix calculus matrix differential equation matrix exponential matrix inversion matrix iteration matrix method matrix multiplication matrix of Equation matrix of order modal matrix mode modulus of rigidity moment of inertia multiplications natural frequencies nonsingular matrix normal coordinates normal modes notation nth-order obtain orthogonal orthogonal matrix oscillations pendulum potential energy power series premultiply problems procedure pulse function quadratic form rational function result ROUTH-HURWITZ STABILITY CRITERION Runge-Kutta Method scalar scalar product Section similarity transformation simultaneous equations singular matrix sinh solution solve square matrix stiffness matrix structure substitute symmetric symmetric matrix therefore transfer matrix transition matrix transmission transmission line transpose trigonometric function unit matrix unit step function vibration whose elements written zero zero matrix