Lie groups | Matrix theory | Exponentials

Matrix exponential

In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems of linear differential equations. In the theory of Lie groups, the matrix exponential gives the exponential map between a matrix Lie algebra and the corresponding Lie group. Let X be an n×n real or complex matrix. The exponential of X, denoted by eX or exp(X), is the n×n matrix given by the power series where is defined to be the identity matrix with the same dimensions as . The above series always converges, so the exponential of X is well-defined. If X is a 1×1 matrix the matrix exponential of X is a 1×1 matrix whose single element is the ordinary exponential of the single element of X. (Wikipedia).

Video thumbnail

Introduction to the Matrix Exponential

In this video we introduce the concept of the matrix exponential. This is similar to the standard exponential function except it operates on matrices. We define the matrix exponential and look at several properties of the matrix exponential that will be very useful in solving systems of

From playlist Ordinary Differential Equations

Video thumbnail

Differential Equations | Matrix Exponential Example: Diagonalizable Case

We present the general form for the matrix exponential of a diagonalizable matrix and a corresponding example. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Systems of Differential Equations

Video thumbnail

(3.8.2) Matrix Exponentials for the General Case: N by N with N Linearly Indep Eigenvectors

This video explains how to find matrix exponentials for the general case when an n by n matrix has n linearly independent eigenvectors. https://mathispower4u.com

From playlist Differential Equations: Complete Set of Course Videos

Video thumbnail

Differential Equations | Matrix Exponential: 2x2 non-diagonalizable case.

We present a general strategy for finding the matrix exponential of a 2x2 matrix that is not diagonalizable. An example is included. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Systems of Differential Equations

Video thumbnail

Exponential Matrix

Today, we take a look at how we can define the exponential of a matrix, or e raised to a matrix, using power series and diagonalisation.

From playlist Linear Algebra

Video thumbnail

Differential Equations | The Matrix Exponential e^{tA}.

We outline a strategy for finding the matrix exponential e^{tA}, including an example when A is 2x2 and not diagonalizable. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Systems of Differential Equations

Video thumbnail

Exponential Growth Models

Introduces notation and formulas for exponential growth models, with solutions to guided problems.

From playlist Discrete Math

Video thumbnail

Use inverse operation to solve exponential equation without one to one property

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations with Logarithms

Video thumbnail

Solving an exponential equation using the one to one property 16^x + 2 = 6

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations with Logarithms

Video thumbnail

Matrix Exponentials | MIT 18.03SC Differential Equations, Fall 2011

Matrix Exponentials Instructor: Lydia Bourouiba View the complete course: http://ocw.mit.edu/18-03SCF11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 18.03SC Differential Equations, Fall 2011

Video thumbnail

(3.8.1) Intro to Matrix Exponentials and Determining Matrix Exponentials for Simple Cases

This video introduces matrix exponentials and the simples cases to determine matrix exponentials. https://mathispower4u.com

From playlist Differential Equations: Complete Set of Course Videos

Video thumbnail

Computing the Matrix Exponential Using the Modal Method

In this video we show how to compute the matrix exponential using the modal method (AKA diagonalization). This involves computing the eigenvalues and eigenvectors of the A matrix and then performing a similarity transformation to diagonalize the A matrix, thereby making the matrix exponen

From playlist Ordinary Differential Equations

Video thumbnail

23. Differential Equations and exp(At)

MIT 18.06 Linear Algebra, Spring 2005 Instructor: Gilbert Strang View the complete course: http://ocw.mit.edu/18-06S05 YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8 23. Differential Equations and exp(At) License: Creative Commons BY-NC-SA More information at

From playlist MIT 18.06 Linear Algebra, Spring 2005

Video thumbnail

Computing the Matrix Exponential Using the Laplace Method

In this video we show how to compute the matrix exponential using the Laplace method. This involves first computing the matrix exponential in the Laplace domain and then performing the inverse Laplace transform to obtain the matrix exponential in the time domain. Topics and timestamps: 0

From playlist Ordinary Differential Equations

Video thumbnail

(3.8.102) Determine a Matrix Exponential and General Solution to x'=Ax: 3 by 3 General Case

This video explains how to determine a matrix exponential for the general case and determine the general solution to x'=Ax. https://mathispower4u.com

From playlist Differential Equations: Complete Set of Course Videos

Video thumbnail

Matrix Factorial?!

Become a Linear Algebra Pro by trying out Brilliant! =D https://brilliant.org/FlammableMaths Complex Numbers but Different Playlist: https://www.youtube.com/playlist?list=PLN2B6ZNu6xmcg3R4wfUlIxtfgtr-2GYAm Today we are going to take the factorial of a matrix and see what we are going to g

From playlist Linear Algebra

Video thumbnail

Coding the matrix exponential on so(3)

For the code described in this video, see https://gist.github.com/Nikolaj-K/7d2cb3452c35c9e2cd09fa6d3bc23498

From playlist Programming

Video thumbnail

Guido Montúfar : Fisher information metric of the conditional probability politopes

Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the September 01, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent

From playlist Geometry

Video thumbnail

Learn basics for solving an exponential equation by using one to one property

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations with Logarithms

Related pages

Derivative of the exponential map | Rotation matrix | Commutator | Lie group | SciPy | Characteristic polynomial | Diagonalizable matrix | Matrix exponential | Exponential map (Lie theory) | Hermitian matrix | Vector flow | Resolvent formalism | Group (mathematics) | Defective matrix | Identity matrix | Interpolation | Lie product formula | Entire function | Matrix norm | Minimal polynomial (linear algebra) | Polynomial evaluation | Sylvester's formula | Trigonometric functions of matrices | Jacobi's formula | Diagonal matrix | Skew-Hermitian matrix | Conjugate transpose | Exponential function | GNU Octave | Vandermonde matrix | Companion matrix | Nilpotent matrix | Euler's rotation theorem | Directional derivative | General linear group | Cayley–Hamilton theorem | Euler's formula | Integrating factor | Laplace transform | Linear differential equation | Meromorphic function | Zero matrix | Ansatz | Laurent series | Tangent vector | Mathematics | Baker–Campbell–Hausdorff formula | Magnus expansion | C0-semigroup | Ordinary differential equation | Matrix differential equation | Real number | Power series | Square matrix | Surjective function | Lie algebra | Projection (linear algebra) | Symmetric matrix | Unitary matrix | Orthogonal matrix | Padé approximant | Complex number | Jordan normal form | Transpose | Golden–Thompson inequality | Variation of parameters | Trace identity | Skew-symmetric matrix | Matrix (mathematics) | Frobenius covariant | Projection matrix | Jordan–Chevalley decomposition | Invertible matrix | Phase-type distribution