Is there any direct proof to show that if eigenvalues of an LTI system are negative then the transition matrix ( or matrix exponential with respect to time) e^{At} decays to zero when t goes to infinity? An straightforward case is when the system is diagonalizable.
2026-02-23 02:38:24.1771814304
Matrix exponential of an LTI system
129 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in LINEAR-ALGEBRA
- An underdetermined system derived for rotated coordinate system
- How to prove the following equality with matrix norm?
- Alternate basis for a subspace of $\mathcal P_3(\mathbb R)$?
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- Why is necessary ask $F$ to be infinite in order to obtain: $ f(v)=0$ for all $ f\in V^* \implies v=0 $
- I don't understand this $\left(\left[T\right]^B_C\right)^{-1}=\left[T^{-1}\right]^C_B$
- Summation in subsets
- $C=AB-BA$. If $CA=AC$, then $C$ is not invertible.
- Basis of span in $R^4$
- Prove if A is regular skew symmetric, I+A is regular (with obstacles)
Related Questions in MATRIX-EXPONENTIAL
- Computing the logarithm of an exponentiated matrix?
- proof of $e^{(A+B)t}=e^{At}e^{Bt}$
- Exponentiation in tensor product of Hilbert spaces
- Matrix exponentiation for given recurrence relation
- Some questions about a $3 \times 3 $ real skew-symmetric matrix
- Solving non-homogeneous matrix exponential problem
- Show that $\exp: \mathfrak h \to \mathfrak H$ is a bijection.
- Matrix exponential, containing a thermal state
- The exponential function and one-parameter subgroups
- Finding the solution to a non-homogeneous matrix exponential.
Related Questions in TRANSITION-MATRIX
- Transition probabilities for many-states Markov model
- Markov Chain - find missing transition values
- Find the transition matrix $P_{S\leftarrow T}$
- A vector $\mathbf{x}\in X$ has coordinates $\mathbf{x}_\mathcal{B}= \langle2,-7,-10\rangle$. What is $\mathbf{x}_\mathcal{G}$?
- A vector $x∈X$ has coordinates $x_B=⟨2,−7,−10⟩$. What is $x_J$?
- transition rates from transition probabilities
- Trying to grasp how to compute a $n$-step transition probability
- Change of Basis Given 2 Vectors and Transition Matrix
- What is the difference between a transition function and a transition kernel?
- Markov chain constant transition matrix
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?