9.1 matrix of a quad form
... (b) What new basis is involved when you use variables X and Y. (c) Find q in terms of X and Y again using the basis changing rule for q. (d) Find the (old) matrix for q. What is the connection between q and the old matrix (write an equation beginning "q = "). (e) Find the new matrix for q. What is t ...
... (b) What new basis is involved when you use variables X and Y. (c) Find q in terms of X and Y again using the basis changing rule for q. (d) Find the (old) matrix for q. What is the connection between q and the old matrix (write an equation beginning "q = "). (e) Find the new matrix for q. What is t ...
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... • The leading/principal diagonal of a matrix is the elements of the diagonal that runs from top left top corner of the matrix to the bottom right as circled in the matrix below. • When all other elements of a matrix are zero except the elements of the leading diagonal, the matrix is referred to as a ...
... • The leading/principal diagonal of a matrix is the elements of the diagonal that runs from top left top corner of the matrix to the bottom right as circled in the matrix below. • When all other elements of a matrix are zero except the elements of the leading diagonal, the matrix is referred to as a ...
Cartesian tensor
In geometry and linear algebra, a Cartesian tensor uses an orthonormal basis to represent a tensor in a Euclidean space in the form of components. Converting a tensor's components from one such basis to another is through an orthogonal transformation.The most familiar coordinate systems are the two-dimensional and three-dimensional Cartesian coordinate systems. Cartesian tensors may be used with any Euclidean space, or more technically, any finite-dimensional vector space over the field of real numbers that has an inner product.Use of Cartesian tensors occurs in physics and engineering, such as with the Cauchy stress tensor and the moment of inertia tensor in rigid body dynamics. Sometimes general curvilinear coordinates are convenient, as in high-deformation continuum mechanics, or even necessary, as in general relativity. While orthonormal bases may be found for some such coordinate systems (e.g. tangent to spherical coordinates), Cartesian tensors may provide considerable simplification for applications in which rotations of rectilinear coordinate axes suffice. The transformation is a passive transformation, since the coordinates are changed and not the physical system.