Notes on k-wedge vectors, determinants, and characteristic
... Although the Cayley–Hamilton theorem does hold over arbitrary fields (including weird ones like F2 ), we will only prove it for real and complex operators. For complex operators this will be easy, once we know that every complex operator is upper-triangular w.r.t. some basis. Proposition 4.5. If T ∈ ...
... Although the Cayley–Hamilton theorem does hold over arbitrary fields (including weird ones like F2 ), we will only prove it for real and complex operators. For complex operators this will be easy, once we know that every complex operator is upper-triangular w.r.t. some basis. Proposition 4.5. If T ∈ ...
Linear codes, generator matrices, check matrices, cyclic codes
... The underlying mechanism: The big trick in study of cyclic codes is to realize that the cycling forward has a useful interpretation in terms of polynomial algebra. Interpret a length n vector v = (v0 , v1 , . . . , vn−1 ) as a polynomial p(x) = vo +v1 x+v2 x2 +. . .+vn−2 xn−2 +vn−1 xn−1 with coeffi ...
... The underlying mechanism: The big trick in study of cyclic codes is to realize that the cycling forward has a useful interpretation in terms of polynomial algebra. Interpret a length n vector v = (v0 , v1 , . . . , vn−1 ) as a polynomial p(x) = vo +v1 x+v2 x2 +. . .+vn−2 xn−2 +vn−1 xn−1 with coeffi ...
MATH 240 – Spring 2013 – Exam 1
... There are five questions. Answer each question on a separate sheet of paper. Use the back side if necessary. On each sheet, put your name, your section TA’s name and your section meeting time. You may assume given matrix equations are well defined (i.e. the matrix sizes are compatible). ...
... There are five questions. Answer each question on a separate sheet of paper. Use the back side if necessary. On each sheet, put your name, your section TA’s name and your section meeting time. You may assume given matrix equations are well defined (i.e. the matrix sizes are compatible). ...
• Perform operations on matrices and use matrices in applications. o
... Perform operations on matrices and use matrices in applications. o MCC9-‐12.N.VM.6 (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. o MCC9-‐1 ...
... Perform operations on matrices and use matrices in applications. o MCC9-‐12.N.VM.6 (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. o MCC9-‐1 ...
Escalogramas multidimensionales
... The matrix of products Q is closely related to the distance matrix , D, we are interested in. The relation between D and Q is as follows : Elements of Q: ...
... The matrix of products Q is closely related to the distance matrix , D, we are interested in. The relation between D and Q is as follows : Elements of Q: ...
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.