Clifford algebras | Historical treatment of quaternions
In mathematics, a split-biquaternion is a hypercomplex number of the form where w, x, y, and z are split-complex numbers and i, j, and k multiply as in the quaternion group. Since each coefficient w, x, y, z spans two real dimensions, the split-biquaternion is an element of an eight-dimensional vector space. Considering that it carries a multiplication, this vector space is an algebra over the real field, or an algebra over a ring where the split-complex numbers form the ring. This algebra was introduced by William Kingdon Clifford in an 1873 article for the London Mathematical Society. It has been repeatedly noted in mathematical literature since then, variously as a deviation in terminology, an illustration of the tensor product of algebras, and as an illustration of the direct sum of algebras.The split-biquaternions have been identified in various ways by algebraists; see below. (Wikipedia).
Using a set of points determine if the figure is a parallelogram using the midpoint formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships
What is a split function?: Dr Chris Tisdell Live Stream
Split functions follow one rule and the swtich to another rule, depending on where you are on a x-axis. I define what a split function is (also called a picewise defined function) and discuss and example. In mathematics, functions are an important tool for understanding how things depend
From playlist Calculus for Beginners
What is the difference of a trapezoid and an isosceles trapezoid
👉 Learn how to solve problems with trapezoids. A trapezoid is a four-sided shape (quadrilateral) such that one pair of opposite sides are parallel. Some of the properties of trapezoids are: one pair of opposite sides are parallel, etc. A trapezoid is isosceles is one pair of opposite sides
From playlist Properties of Trapezoids
Determine if a set of points is a parallelogram using the distance formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
CCSS What is an angle bisector
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships
Split Complex Numbers in Matrix Form
In this video, we'll find the matrix representation for the split complex numbers, which are those numbers similar to the complex numbers but with an imaginary unit, j, which squares to 1 instead of -1. We will also review Euler's formula for the split complex numbers and how this relates
From playlist Math
Determining if a set of points makes a parallelogram or not
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Determine if a set of points makes up a rectangle using the distance formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Forward Stock Splits vs Reverse Stock Splits - Stock Trading 101
This video on stock trading explains the difference between forward stock splits and reverse stock splits. In a forward stock split, the number of outstanding shares increases and the price of the stock decreases by the same factor such as that the market capitalization of the company rem
From playlist Stocks and Bonds
What is the Best Way to Split Text in Excel?
Sign up for our Excel webinar, times added weekly: https://www.excelcampus.com/blueprint-registration/ In this video, you can learn the pros and cons of the new text splitting functions in Excel. If you’d like to read the accompanying blog post on my website, you can access it here: https
From playlist Excel Formulas
Periodicity and crystal field theory
IB Chemistry Lesson on why coloured transition metal complexes form.
From playlist IB Chemistry
Galois theory: Splitting fields
This lecture is part of an online course on Galois theory. We define the splitting field of a polynomial p over a field K (a field that is generated by roots of p and such that p splits into linear factors). We give a few examples, and show that it exists and is unique up to isomorphism
From playlist Galois theory
Chemistry 51A: Organic Chemistry. Lecture 27
UCI Chem 51A Organic Chemistry (Fall 2014) Lec 27. Organic Chemistry -- Spin-Spin Coupling View the complete course: http://ocw.uci.edu/courses/chem_51a_organic_chemistry.html Instructor: Susan King, Ph.D. License: Creative Commons BY-NC-SA Terms of Use: http://ocw.uci.edu/info. More cou
From playlist Chemistry 51A: Organic Chemistry
A non-linear spinor theory of elementary particles
This presentation is about a non-linear spinor theory of elementary particles developed by Norbert Winter, an elementary particle physicist and former employee of the Max-Planck Institute for Physics in Munich, Germany. The idea of a non-linear theory of elementary particles dates back to
From playlist Summer of Math Exposition Youtube Videos
Introduction to Interpretable Machine Learning II - Cynthia Rudin
2022 Program for Women and Mathematics: The Mathematics of Machine Learning Topic: Terng Lecture: Introduction to Interpretable Machine Learning II Speaker: Cynthia Rudin Affiliation: Duke University Date: May 24, 2022
From playlist Mathematics
Learning To See [Part 14: Better Heuristics]
In this series, we'll explore the complex landscape of machine learning and artificial intelligence through one example from the field of computer vision: using a decision tree to count the number of fingers in an image. It's gonna be crazy. Supporting Code: https://github.com/stephencwe
From playlist Learning To See
How to determine if a set of points makes up a rectangle using the distance formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane