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To linearize a system, in one of the steps I am required to find the fundamental matrix $\Phi$(t) of a system such that $\Phi$(0)=I. The example system my professor used: $\dot{x} = x - y - x^3 - ... 1answer 6 views ### When is the solution to a n initial value problem matrix differential equation invertible? Suppose$A (t,s)$a$n\times n$matrix is the solution of the initial value problem below, where$B_s$is also an$n\times n$matrix, invertible for all$s$: $$\dfrac{d A(t,s)}{ds} = B_s A(t,s)$$ $$... 0answers 25 views ### Derivative with respect to a function We have a function {f(s,{\psi(s)}_{3\times 1})}_{3\times1}\tag1 Given Data f,\psi are matrices and their dimensions are already given in the question s is not a matrix, it is a scalar ... 0answers 36 views ### Transpose/multiplication of 3D matrices I have A(p)=\begin{bmatrix}p_1 &p_2 & p_3\\ 2p_1 &2p_2^2 & 4p_3^3\\ 3p_1 &3p_1 & 10\\ \end{bmatrix}\tag 1 p= {\left(\begin{array}{c}p_1\\p_2\\p_3\\p_4 ... 0answers 21 views ### Matrix Algebra - Linear dependency We have a given equation \frac{\mathrm{d}R(t) }{\mathrm{d} t}=R(t) \{(1-t)U_0+t U_1\}\tag 1, all variables except scalar variable 't' has dimension 3 \times 3. Given data R(t) is ... 1answer 45 views ### Matrix - Commutative property I have a rotation matrix represented as R(t)=e^{B(t)},\tag 1 where B(t) is a skew symmetric matrix (since any rotation matrix can be expressed as a matrix exponent of a skew symmetric matrix), ... 0answers 28 views ### Diagonalize Complex ODE I'm trying to solve for the dynamics of one coordinate of a coupled system of linear differential equations with complex coefficients. Physically, a number of single-pole harmonic oscillators with ... 1answer 28 views ### Matrix Solution I have matrix integral equation of the following form {f^{'}(x)}_{1 \times 1}A_{3\times 3}=P_{3\times3} (1-x)+Q_{3 \times 3}x \tag 1 . All dimensions are indicated in equation itself. " ' " ... 1answer 59 views ### Matrix-valued differential equation A'(t)=A(t)B(t) How to solve matrix-valued differential equations of type$$A'(t)=A(t)B(t) \tag 1$$All the given functions are square matrices of dimension 3 and only A(t) is invertible (not B(t) or ... 0answers 62 views ### Matrix exponent form We have an equation of matrix exponent Ae^{Ax}R-e^{Ax}R (P_1 +P_2 x) = Y \tag1 Given condition A,R,P_1,P_2,Y are constant 3 \times 3 matrices. R is invertible,orthonormal,determinent ... 0answers 53 views ### Converting a series to a recursive expression Let e_i be a unit vector with one 1 in the i-th element. Is the following expression has a recursive presentation?$$y = \sum_{k=0}^{\infty} {\frac{{{X^k} e_i}}{\|{{{X^k} e_i}\|}_2}} $$where ... 3answers 66 views ### Conversion of rotation matrix to quaternion We use unit length Quaternion to represent rotations. Following is a general rotation matrix obtained {\begin{bmatrix}m_{00} & m_{01}&m_{02} \\ m_{10} & m_{11}&m_{12}\\ m_{20} & ... 0answers 30 views ### Tool for differentiating a matrix and solving a matrix equation (in closed-form)? Is there any software or online tool that can analytically solve a complex matrix equation, such as the following one in closed form (not numerically)?$$\frac{\partial \; ... 0answers 15 views ### using ode45 for descriptive forms Using Matlab what would be the most efficient way to solve,$A_1x'(t) = A_2x(t)$, where both$A_1$and$A_2$are$n\times n$matrices. Both are sparse matrices and hence I want to avoid inversion. ... 0answers 38 views ### Finding a solution basis of differential equation Find a solution basis of $$y'=\left[ \begin{matrix}3&-4&-2\\2&-3&-2\\0&0&1\\ \end{matrix} \right]y \,\text{ and find the solution } \Phi \text{ with } \Phi(0) = (1,1,1).$$ I'm ... 0answers 78 views ### Quaternion conversion We have a normalized orthogonal co-ordinate frame travelling through the curve as in figure 1 below, from one end to other. Let us call starting end as A and ending end as B. What we know is initial ... 1answer 45 views ### First-order linear differential equation for matrix valued functions of size$3\times 3$I have two matries given by (M' means derivative w.r.t x)$ M=\left( \begin{array}{ccc} f_1(x) & f_2(x) & f_3(x) \\ f_4(x) & f_5(x)& f_6(x) \\ f_7(x) & f_8(x) & ...
Given data and conditions I have a power series, $PS(x) = \sum_{n=0}^\infty R_nx^n$. I have a infinite GP,something like G(x) = $\sum_{k=0}^\infty ax^k = \frac{a}{1-x}$ . Never take G(x),such ...