This chapter extends several functional equations to the case of vector or matrix equations of vector or matrix variables. In some cases, there is a direct extension because the properties of groups can be made use of, but in others, this extension is much more complicated or becomes ...
Matrix Equation A matrix equation (also called a matrix–vector equation) is an equation of the form Av = b, where A is an m-by-n matrix, called the coefficient matrix, v is an n-by-1 column vector, and b is an m-by-1 column vector. Illustration ■ A matrix equation with a 2...
Specify the independent variables x(t), y(t), and z(t) in the equations as a symbolic vector vars. Use the equationsToMatrix function to convert the system of equations into the matrix form. Get vars = [x(t); y(t); z(t)]; [A,b] = equationsToMatrix(eqn,vars) A = ⎛...
【题目】The vector equation of the line L is given by$$ \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} - 3 \\ 0 \\ 8 \end{bmatrix} + t \begin{bmatrix} 4 \\ - 1 \\ - 3 \end{bmatrix} $$Show that A(5,-3,2) is the foot of the perpendicular ...
1) Calculate the trace(the sum of the diagonal elements) of the matrix T from the equation: T = 4 - 4*qx2- 4*qy2- 4*qz2 = 4( 1 -qx2- qy2- qz2) = m00 + m11 + m22 + 1 If the trace of the matrix is greater than zero, then the result is: ...
1 \end{matrix} ) $$where u and v are parameters.The line L has vector equation$$ r = \left[ \begin{matrix} 2 \\ 1 \\ - 3 \end{matrix} \right] + \left[ \begin{matrix} 2 \\ 3 \\ - 4 \end{matrix} \right] $$where t is a parameter.Show that L is parallel to II...
A1(x), . . . ,AK(x) on its diagonal. Hence multiple LMI constraints can be imposed on the vector of decision variablesxwithout destroying convexity. In most control applications, LMIs do not naturally arise in the canonical form ofEquation 1, but rather in the form ...
Moreusefully,KVLisexpressedbytheequation T bn uAu whereu b =[u 1 u 2 ...u b ] T isthebranchvoltagevector,u n =[u ① u ② ...u n 1 ] T is thenode-to-datumvoltagevector,andA T isab*(n 1)matrix. TheTypicalBranch R k u Sk i Sk i k u k ,1,2,, kkkkSkSk iGuGuikb ...
The previous example was helpful for presenting the dimensional analysis validation, but the equation itself only contained scalar operation. We will show here how vector, spinor, and matrix operations can be combined in a compact syntax to perform advanced calculations. In this example we reproduce...
It is seldom necessary to form the explicit inverse of a matrix. A frequent misuse ofinvarises when solving the system of linear equationsAx=b. One way to solve the equation is withx = inv(A)*b. A better way, from the standpoint of both execution time and numerical accuracy, is to ...