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VECTORS AND MATRICES
The matrix element of arc and the element of area in the plane
The canonical form of a linear operator
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3X1 matrix a-axis applied force area dSx c-axis Cartesian reference frame coefficients column vector compatibility relations complex number compression cylinder deformable medium denote derivatives diagonal matrix differential diva elastically insensitive element of area elements of 77 energy of deformation equivalently Exercise final rectangular Cartesian follows force per unit formula given rotation Hence Hint hydrostatic pressure independent variables infinitesimal theory initial rectangular Cartesian initial stress integrated linear theory isotropic Jacobian matrix linear combination linear function linear vector operator magnitude matrix dx matrix element medium is elastically medium possesses multiplication non-singular obtain polar coordinates portion Vx principal axes R*TR rectangular Cartesian reference respect rotation matrix row vector second-order approximation second-order elastic constants shear Show simple shear square matrix strain matrix 77 stress matrix symmetric matrix tension theory of elasticity third-order elastic constants transpose unit initial area unitary matrix virtual deformation Young's modulus zero