Matrices | Mathematical terminology

Generalized inverse

In mathematics, and in particular, algebra, a generalized inverse (or, g-inverse) of an element x is an element y that has some properties of an inverse element but not necessarily all of them. Generalized inverses can be defined in any mathematical structure that involves associative multiplication, that is, in a semigroup. This article describes generalized inverses of a matrix . A matrix is a generalized inverse of a matrix if The purpose of constructing a generalized inverse of a matrix is to obtain a matrix that can serve as an inverse in some sense for a wider class of matrices than invertible matrices. A generalized inverse exists for an arbitrary matrix, and when a matrix has a , this inverse is its unique generalized inverse. (Wikipedia).

Video thumbnail

Math 030 Calculus I 031315: Inverse Functions and Differentiation

Inverse functions. Examples of determining the inverse. Relation between the graphs of a function and its inverse. One-to-one functions. Restricting the domain of a function so that it is invertible. Differentiability of inverse functions; relation between derivatives of function and

From playlist Course 2: Calculus I

Video thumbnail

Step by step find the inverse of the reciprocal function

👉 Learn how to find the inverse of a rational function. A rational function is a function that has an expression in the numerator and the denominator of the function. The inverse of a function is a function that reverses the "effect" of the original function. One important property of the

From playlist Find the Inverse of a Function

Video thumbnail

Graphing and finding the inverse of a rational function

👉 Learn how to find the inverse of a rational function. A rational function is a function that has an expression in the numerator and the denominator of the function. The inverse of a function is a function that reverses the "effect" of the original function. One important property of the

From playlist Find the Inverse of a Function

Video thumbnail

How to write the inverse of a function when it is a fraction

👉 Learn how to find the inverse of a rational function. A rational function is a function that has an expression in the numerator and the denominator of the function. The inverse of a function is a function that reverses the "effect" of the original function. One important property of the

From playlist Find the Inverse of a Function

Video thumbnail

Learn the steps to finding the inverse of the reciprocal function

👉 Learn how to find the inverse of a rational function. A rational function is a function that has an expression in the numerator and the denominator of the function. The inverse of a function is a function that reverses the "effect" of the original function. One important property of the

From playlist Find the Inverse of a Function

Video thumbnail

Use the inverse of a function to determine the domain and range

👉 Learn how to find the inverse of a linear function. A linear function is a function whose highest exponent in the variable(s) is 1. The inverse of a function is a function that reverses the "effect" of the original function. One important property of the inverse of a function is that whe

From playlist Find the Inverse of a Function

Video thumbnail

How to determine if a rational function has an inverse and what it is

👉 Learn how to find the inverse of a rational function. A rational function is a function that has an expression in the numerator and the denominator of the function. The inverse of a function is a function that reverses the "effect" of the original function. One important property of the

From playlist Find the Inverse of a Function

Video thumbnail

How to find the inverse and then determine if the inverse is a function

👉 Learn how to find the inverse of a quadratic function. A quadratic function is a function whose highest exponent in the variable(s) of the function is 2. The inverse of a function is a function that reverses the "effect" of the original function. One important property of the inverse of

From playlist Find the Inverse of a Function

Video thumbnail

How to find the inverse of a quadratic equation

👉 Learn how to find the inverse of a quadratic function. A quadratic function is a function whose highest exponent in the variable(s) of the function is 2. The inverse of a function is a function that reverses the "effect" of the original function. One important property of the inverse of

From playlist Find the Inverse of a Function

Video thumbnail

Modular Inverses, Generators, and Order: Linking Elementary Number Theory and Abstract Algebra

Solution to the unique number question posed at 5:01 We show two solution: one is more informal using intuition, and the other using congruences 1) Using Intuition We use a proof by contradiction: suppose that you can reach the same number twice WITHOUT first cycling back to 0. But since y

From playlist Summer of Math Exposition Youtube Videos

Video thumbnail

Abstract Algebra April 20

Suggest a problem: https://forms.gle/ea7Pw7HcKePGB4my5 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.michael-penn.net Randolph College Math: http://www.randolphcollege.edu/ma

From playlist Super Lo-fi in class videos

Video thumbnail

Cosets -- Abstract Algebra video 9

⭐Support the channel⭐ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn 🟢 Discord: https://discord.gg/Ta6PTGtKBm ⭐my other channels⭐ Main Channel: https://www.youtube.

From playlist Abstract Algebra

Video thumbnail

Some general results on groups -- Abstract Algebra 6

⭐Support the channel⭐ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn 🟢 Discord: https://discord.gg/Ta6PTGtKBm ⭐my other channels⭐ Main Channel: https://www.youtube.

From playlist Abstract Algebra

Video thumbnail

Integrals of Inverses - A General Formula!

Patreon: https://www.patreon.com/whatthehectogon Instagram: https://www.instagram.com/whatthehectogon/ Doggo: https://www.instagram.com/fluffy.gus/ Email: whatthehectagon@gmail.com

From playlist WACKY integrals

Video thumbnail

Transposes and Inverses II | Linear Algebra MATH1141 | N J Wildberger

We introduce the notion of the inverse of an n by n matrix. Concrete formulas for the 1 by 1 and the 2 by 2 cases are given, and we derive various useful properties. ************************ Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a co

From playlist Higher Linear Algebra

Video thumbnail

Researchers Use Group Theory to Speed Up Algorithms — Introduction to Groups

This is the most information-dense introduction to group theory you'll see on this website. If you're a computer scientist like me and have always wondered what group theory is useful for and why it even exists and furthermore don't want to bother spending hours learning the basics, this i

From playlist Summer of Math Exposition 2 videos

Video thumbnail

Normal Subgroups and Quotient Groups -- Abstract Algebra 11

⭐Support the channel⭐ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn 🟢 Discord: https://discord.gg/Ta6PTGtKBm ⭐my other channels⭐ Main Channel: https://www.youtube.

From playlist Abstract Algebra

Video thumbnail

Jacobian chain rule and inverse function theorem

A lecture that discusses: the general chain rule for the Jacobian derivative; and the inverse function theorem. The concepts are illustrated via examples and are seen in university mathematics.

From playlist Several Variable Calculus / Vector Calculus

Video thumbnail

How to find the inverse of a direct variation function

👉 Learn how to find the inverse of a linear function. A linear function is a function whose highest exponent in the variable(s) is 1. The inverse of a function is a function that reverses the "effect" of the original function. One important property of the inverse of a function is that whe

From playlist Find the Inverse of a Function

Related pages

Identity matrix | Rank factorization | Algebra | Semigroup | Mathematical structure | Block matrix pseudoinverse | Multiplication | System of linear equations | Associative property | Mathematics | Regular semigroup | Moore–Penrose inverse | Square matrix | Ring (mathematics) | E. H. Moore | Drazin inverse | Inverse element | Matrix (mathematics) | Invertible matrix