Unary operations | Multiplication | Abstract algebra | Elementary algebra | Elementary special functions
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the function f(x) that maps x to 1/x, is one of the simplest examples of a function which is its own inverse (an involution). Multiplying by a number is the same as dividing by its reciprocal and vice versa. For example, multiplication by 4/5 (or 0.8) will give the same result as division by 5/4 (or 1.25). Therefore, multiplication by a number followed by multiplication by its reciprocal yields the original number (since the product of the number and its reciprocal is 1). The term reciprocal was in common use at least as far back as the third edition of Encyclopædia Britannica (1797) to describe two numbers whose product is 1; geometrical quantities in inverse proportion are described as reciprocall in a 1570 translation of Euclid's Elements. In the phrase multiplicative inverse, the qualifier multiplicative is often omitted and then tacitly understood (in contrast to the additive inverse). Multiplicative inverses can be defined over many mathematical domains as well as numbers. In these cases it can happen that ab ≠ ba; then "inverse" typically implies that an element is both a left and right inverse. The notation f −1 is sometimes also used for the inverse function of the function f, which is for most functions not equal to the multiplicative inverse. For example, the multiplicative inverse 1/(sin x) = (sin x)−1 is the cosecant of x, and not the inverse sine of x denoted by sin−1 x or arcsin x. The terminology difference reciprocal versus inverse is not sufficient to make this distinction, since many authors prefer the opposite naming convention, probably for historical reasons (for example in French, the inverse function is preferably called the bijection réciproque). (Wikipedia).
Review of Multiplicative Inverses
In this video we connect and review the ideas of multiplicative inverses and reciprocals
From playlist Middle School This Year
Linear Algebra - Lecture 23 - The Inverse of a Matrix
In this lecture, we'll learn about the multiplicative inverse of a matrix. We'll discuss inverses of 2x2 matrices, as well as properties of inverses.
From playlist Linear Algebra Lectures
Inverse Matrices & Matrix Equations 4 Ex Multiplicative Inverses Full Length
I start by defining the Multiplicative Identity Matrix and a Multiplicative Inverse of a Square Matrix. I then work through three examples finding an Inverse Matrix. Inverse of 2 x 2 Matrix at 5:14 and 14:50 Inverse of a 3 x 3 Matrix at 21:32 Matrix Equation example at 39:58 Check out
From playlist Linear Algebra
Multiplicative Inverse and Reciprocals
http://www.youtube.com/view_play_list?p=8E39E839B4C6B1DE
From playlist Common Core Standards - 6th Grade
👉 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
Learn 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
Learn 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
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
Our first examples of groups -- Abstract Algebra 3
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From playlist Abstract Algebra
The modular inverse via Gauss not Euclid
We demonstrate a lesser-known algorithm for taking the inverse of a residue modulo p, where p is prime. This algorithm doesn't depend on the extended Euclidean algorithm, so it can be learned independently. This is part of a larger series on modular arithmetic: https://www.youtube.com/pl
From playlist Modular Arithmetic Visually
What is a Tensor? Lesson 19: Algebraic Structures I
What is a Tensor? Lesson 19: Algebraic Structures Part One: Groupoids to Fields This is a redo or a recently posted lesson. Same content, a bit cleaner. Algebraic structures are frequently mentioned in the literature of general relativity, so it is good to understand the basic lexicon of
From playlist What is a Tensor?
All About Subgroups | Abstract Algebra
We introduce subgroups, the definition of subgroup, examples and non-examples of subgroups, and we prove that subgroups are groups. We also do an example proving a subset is a subgroup. If G is a group and H is a nonempty subset of G, we say H is a subgroup of G if H is closed with respect
From playlist Abstract Algebra
Abstract Algebra - 2.3 Elementary Properties of a Group
We look closely at a few of the properties of groups and their proofs, including cancellation, uniqueness of inverses and identities and the socks-shoes property. We will utilize the WTS, Given, Proof format for our proofs. We will also compare the multiplicative and additive notations and
From playlist Abstract Algebra - Entire Course
Abstract Algebra | What is a ring?
We give the definition of a ring and present some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
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
A Short Course in Algebra and Number Theory - Fields
To supplement a course taught at The University of Queensland's School of Mathematics and Physics I present a very brief summary of algebra and number theory for those students who need to quickly refresh that material or fill in some gaps in their understanding. This is the third lectur
From playlist A Short Course in Algebra and Number Theory
Learn how to step by step find the inverse of a quadratic 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