Matrices

Drazin inverse

In mathematics, the Drazin inverse, named after Michael P. Drazin, is a kind of generalized inverse of a matrix. Let A be a square matrix. The index of A is the least nonnegative integer k such that rank(Ak+1) = rank(Ak). The Drazin inverse of A is the unique matrix AD that satisfies It's not a generalized inverse in the classical sense, since in general. * If A is invertible with inverse , then . * Drazin inversion is invariant under conjugation. If is the Drazin inverse of , then is the Drazin inverse of . * The Drazin inverse of a matrix of index 0 or 1 is called the group inverse or {1,2,5}-inverse and denoted A#. The group inverse can be defined, equivalently, by the properties AA#A = A, A#AA# = A#, and AA# = A#A. * A projection matrix P, defined as a matrix such that P2 = P, has index 1 (or 0) and has Drazin inverse PD = P. * If A is a nilpotent matrix (for example a shift matrix), then The hyper-power sequence is for convergence notice that For or any regular with chosen such that the sequence tends to its Drazin inverse, (Wikipedia).

Video thumbnail

What's New in Calculus & Algebra

I will give an overview of recent and upcoming features related to calculus and algebra in the Wolfram Language. These features include support for interval computation in more than one hundred mathematical functions, powerful new techniques for evaluating integrals of algebraic functions,

From playlist Wolfram Technology Conference 2021

Video thumbnail

Composition of inverses using a triangle with variables

๐Ÿ‘‰ Learn how to evaluate an expression with the composition of a function and a function inverse. Just like every other mathematical operation, when given a composition of a trigonometric function and an inverse trigonometric function, you first evaluate the one inside the parenthesis. We

From playlist Evaluate a Composition of Inverse Trigonometric Functions

Video thumbnail

What are the Inverse Trigonometric functions and what do they mean?

๐Ÿ‘‰ Learn how to evaluate inverse trigonometric functions. The inverse trigonometric functions are used to obtain theta, the angle which yielded the trigonometric function value. It is usually helpful to use the calculator to calculate the inverse trigonometric functions, especially for non-

From playlist Evaluate Inverse Trigonometric Functions

Video thumbnail

Using composition of inverses using triangles

๐Ÿ‘‰ Learn how to evaluate an expression with the composition of a function and a function inverse. Just like every other mathematical operation, when given a composition of a trigonometric function and an inverse trigonometric function, you first evaluate the one inside the parenthesis. We

From playlist Evaluate a Composition of Inverse Trigonometric Functions

Video thumbnail

0134 [ C++/React ] Moderation tools for a multi-player game server

This is #134 in my series of live (Twitch) coding streams. This stream I continued my work on developing various aspects of the moderation system for my game. Notebook page: https://tinyurl.com/y47mbpyb -- Watch live at https://www.twitch.tv/rhymu8354

From playlist Excalibur

Video thumbnail

Using triangles to evaluate for compositions of inverse functions

๐Ÿ‘‰ Learn how to evaluate an expression with the composition of a function and a function inverse. Just like every other mathematical operation, when given a composition of a trigonometric function and an inverse trigonometric function, you first evaluate the one inside the parenthesis. We

From playlist Evaluate a Composition of Inverse Trigonometric Functions

Video thumbnail

Evaluating the composition of inverse functions using triangles

๐Ÿ‘‰ Learn how to evaluate an expression with the composition of a function and a function inverse. Just like every other mathematical operation, when given a composition of a trigonometric function and an inverse trigonometric function, you first evaluate the one inside the parenthesis. We

From playlist Evaluate a Composition of Inverse Trigonometric Functions

Video thumbnail

Evaluate the inverse trig with composition

๐Ÿ‘‰ Learn how to evaluate an expression with the composition of a function and a function inverse. Just like every other mathematical operation, when given a composition of a trigonometric function and an inverse trigonometric function, you first evaluate the one inside the parenthesis. We

From playlist Evaluate a Composition of Inverse Trigonometric Functions

Video thumbnail

Learn the steps to evaluating the composition of inverse trig functions

๐Ÿ‘‰ Learn how to evaluate an expression with the composition of a function and a function inverse. Just like every other mathematical operation, when given a composition of a trigonometric function and an inverse trigonometric function, you first evaluate the one inside the parenthesis. We

From playlist Evaluate a Composition of Inverse Trigonometric Functions

Video thumbnail

9A_2 The Inverse of a Matrix Using the Idenity Matrix

The inverse of a matrix using the method of elementary row operation with an identity matrix added to the matrix.

From playlist Linear Algebra

Video thumbnail

[Linear Algebra] Solving with Inverses and Inverse Properties

We solve systems of equations using inverse identities LIKE AND SHARE THE VIDEO IF IT HELPED! Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW Like us on Facebook: http://on.fb.me/1vWwDRc Submit your questions on Reddit: http://bit.ly/1GwZZrP #LinearA

From playlist Linear Algebra

Video thumbnail

Derivative of Inverse Function 4K

I review the fundamental of Inverse Functions and then work through 3 examples of finding the slope of an inverse function at a given point. Graphical relationship between a function and inverse: 2:28 Defining a one to one function: 6:09 Restricting the domain of a function: 13:50 Comparin

From playlist Calculus (New)

Video thumbnail

Worldwide Calculus: Inverse Trig Functions

Lecture on 'Inverse Trig Functions' from 'Worldwide Differential Calculus' and 'Worldwide AP Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.

From playlist Worldwide Single-Variable Calculus for APยฎ

Video thumbnail

How to Use Inverse Trigonometric Functions (Precalculus - Trigonometry 18)

An in-depth look at how to use inverse trig functions and how they relate to basic trig functions. The domain and range of these functions is also thoroughly discussed. Support: https://www.patreon.com/ProfessorLeonard

From playlist Precalculus - College Algebra/Trigonometry

Video thumbnail

Introduction to Inverse Trigonometric Functions (Precalculus - Trigonometry 17)

What Inverse Trigonometric Functions are, where they come from, and why we need to restrict domain to be able to use them. Special focus will be on the nature of one-to-one functions and how they relate to the common trigonometric functions. Support: https://www.patreon.com/ProfessorLeona

From playlist Precalculus - College Algebra/Trigonometry

Video thumbnail

Calculus 2, inverse functions (Feb 5 2021)

Inverse functions! This is a recording of a live class for Math 1172, Calculus 2, an undergraduate course for math majors at Fairfield University, Spring 2021. Class website: http://cstaecker.fairfield.edu/~cstaecker/courses/2021s1172/

From playlist Math 1172 (Calculus 2) Spring 2021

Video thumbnail

Finding Inverse Functions (Precalculus - College Algebra 51)

Support: https://www.patreon.com/ProfessorLeonard Professor Leonard Merch: https://professor-leonard.myshopify.com How to find the inverse of a one-to-one function and how to restrict the domain to create certain one-to-one functions.

From playlist Precalculus - College Algebra/Trigonometry

Video thumbnail

An Indepth Look at Using Inverse Trig Functions (Precalculus - Trigonometry 21)

A very detailed explanation of Inverse Trigonometric Functions and how to use them in conjunction with Basic Trig Functions. Pretty much all you need to know about using inverse trig functions. Support: https://www.patreon.com/ProfessorLeonard

From playlist Precalculus - College Algebra/Trigonometry

Video thumbnail

Why does inverse trig functions have restrictions Function explanation

๐Ÿ‘‰ Learn how to evaluate inverse trigonometric functions. The inverse trigonometric functions are used to obtain theta, the angle which yielded the trigonometric function value. It is usually helpful to use the calculator to calculate the inverse trigonometric functions, especially for non-

From playlist Evaluate Inverse Trigonometric Functions

Related pages

Generalized inverse | Generalized eigenvector | Jordan normal form | Mathematics | Mooreโ€“Penrose inverse | Shift matrix | Inverse element | Perfect field | Matrix (mathematics) | Projection (linear algebra) | Nilpotent matrix | Constrained generalized inverse