Unary operations | Exponentials | Algebra | Elementary arithmetic | Squares in number theory
In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation. Squaring is the same as raising to the power 2, and is denoted by a superscript 2; for instance, the square of 3 may be written as 32, which is the number 9.In some cases when superscripts are not available, as for instance in programming languages or plain text files, the notations x^2 (caret) or x**2 may be used in place of x2.The adjective which corresponds to squaring is quadratic. The square of an integer may also be called a square number or a perfect square. In algebra, the operation of squaring is often generalized to polynomials, other expressions, or values in systems of mathematical values other than the numbers. For instance, the square of the linear polynomial x + 1 is the quadratic polynomial (x + 1)2 = x2 + 2x + 1. One of the important properties of squaring, for numbers as well as in many other mathematical systems, is that (for all numbers x), the square of x is the same as the square of its additive inverse −x. That is, the square function satisfies the identity x2 = (−x)2. This can also be expressed by saying that the square function is an even function. (Wikipedia).
What’s the difference of two squares?
This is a short animation showing one way to think of the difference of squares formula (at least when the two numbers involved are positive). #manim #math #proofwithoutwords #visualproof
From playlist Algebra
A more in depth discussion on the determinant of a square matrix.
From playlist Linear Algebra
Algebra for Beginners | Basics of Algebra
#Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. Table of Conten
From playlist Linear Algebra
7B Inverse of a Matrix-YouTube sharing.mov
An introduction to the inverse of a square matrix.
From playlist Linear Algebra
find the complex solutions to this quadratic equation by completing the square
Learn how to solve a non-factorable quadratic equation by completing the square. The equation is x^2=12x-45 and it is easier to use the completing the square method than the quadratic formula. We will actually get complex solutions for this quadratic equation. For more algebra tutorials,
From playlist Algebra Basics
Invertible matrices are square
Why invertible matrices must be square. Definition of invertible matrix and showing that a 3x2 and a 2x3 matrix cannot be square. Check out my Matrix Algebra playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmAIZGo2l8SWvsHeeCLzamx0 Subscribe to my channel: https://www.youtube.c
From playlist Matrix Algebra
Square Roots Defined and Examples
I define square roots and then work through examples. Arithmetic Examples 7:32 Application Problem 1 15:12 Application Problem 2 24:10 Find free review test, useful notes and more at http://www.mathplane.com If you'd like to make a donation to support my efforts look for the "Tip the Teach
From playlist Algebra 1
Matrix Algebra Basics || Matrix Algebra for Beginners
In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. This course is about basics of matrix algebra. Website: https://geekslesson.com/ 0:00 Introduction 0:19 Vectors and Matrices 3:30 Identities and Transposes 5:59 Add
From playlist Algebra
A Swift Introduction to Spacetime Algebra
This video is a fast-paced introduction to Spacetime Algebra (STA), which is the geometric algebra of Minkowski space. In it, we figure out what the problems are with the way introductory textbooks usually describe special relativity and how we can solve those problems by using spacetime
From playlist Miscellaneous Math
Geometric Algebra - Rotors and Quaternions
In this video, we will take note of the even subalgebra of G(3), see that it is isomorphic to the quaternions and, in particular, the set of rotors, themselves in the even subalgebra, correspond to the set of unit quaternions. This brings the entire subject of quaternions under the heading
From playlist Math
Can you do this algebra problem? (Simplify a rational expression)
How to simplify a rational expression. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, review notes and quizzes. All cour
From playlist GED Prep Videos
Lie Groups and Lie Algebras: Lesson 29 - SO(3) from so(3)
Lie Groups and Lie Algebras: Lesson 29 - SO(3) from so(3) In this video lesson we construct the Lie group elements of SO(3) starting from the defining property of SO(3) and the Lie algebra of so(3). To do this we review the Caley-Hamilton theorem that a square matrix satisfies its own cha
From playlist Lie Groups and Lie Algebras
LC001.03 - Clifford algebras and matrix factorisations
A brief introduction to Clifford algebras, their universal property, how to construct a Clifford algebra from the Hessian of a quadratic form, and how modules over that Clifford algebra determine matrix factorisations. This video is a recording made in a virtual world (https://www.roblox.
From playlist Metauni
Learn Algebra Formulas – Understand In 18 Minutes
Learn the most important formulas in algebra. Many students struggle with algebra because they don’t really understand how and when to use key formulas when solving math problems. This video will go over the key algebra formulas that each student needs to understand very well. TabletCla
From playlist Algebra
Stable Homotopy Seminar, 18: The Steenrod Algebra (Liam Keenan)
Liam defines the Steenrod algebra, as the endomorphisms of the Eilenberg-MacLane spectrum HF_p. This naturally acts on the mod p cohomology of any space (or spectrum), and we look at the example of the mod 2 cohomology of RP^infinity. He states some of its fundamental properties allowing u
From playlist Stable Homotopy Seminar
The square of a number plus 2 is 38, what is the number(s)?
How to translate a verbal phrase or sentence into an algebraic expression or equation. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printabl
From playlist GED Prep Videos
Algebraic and Transcendental Elements; Finite Extensions - Field Theory - Lecture 01
In this video we introduce the notion of algebraic and transcendental. We then introduce a notion of "finite extension" which will help us prove every element in an extension is algebraic. See @MatthewSalomone's Abstract Algebra 2 videos. They complement this presentation with better exa
From playlist Field Theory
Algebraic geometry 1 Introduction
This lecture is part of an online algebraic geometry course (Berkeley math 256A fall 2020), based on chapter I of "Algebraic geometry" by Hartshorne. The full set of lectures is in the playlist "Algebraic geometry I: varieties". (The course continues in the playlist "Algebraic geometry I
From playlist Algebraic geometry I: Varieties
Algebra 1 11.5a - Expressions Involving Square Roots
From the Algebra 1 course by Derek Owens
From playlist Algebra 1 Chapter 11 (Selected videos)