Vector calculus | Vectors (mathematics and physics) | Linear algebra
In physics and mathematics, a pseudovector (or axial vector) is a quantity that is defined as a function of some vectors or other geometric shapes, that resembles a vector, and behaves like a vector in many situations, but is changed into its opposite if the orientation of the space is changed, or an improper rigid transformation such as a reflection is applied to the whole figure. Geometrically, the direction of a reflected pseudovector is opposite to its mirror image, but with equal magnitude. In contrast, the reflection of a true (or polar) vector is exactly the same as its mirror image. In three dimensions, the curl of a polar vector field at a point and the cross product of two polar vectors are pseudovectors. One example of a pseudovector is the normal to an oriented plane. An oriented plane can be defined by two non-parallel vectors, a and b, that span the plane. The vector a × b is a normal to the plane (there are two normals, one on each side – the right-hand rule will determine which), and is a pseudovector. This has consequences in computer graphics where it has to be considered when transforming surface normals. A number of quantities in physics behave as pseudovectors rather than polar vectors, including magnetic field and angular velocity. In mathematics, in three-dimensions, pseudovectors are equivalent to bivectors, from which the transformation rules of pseudovectors can be derived. More generally in n-dimensional geometric algebra pseudovectors are the elements of the algebra with dimension n − 1, written ⋀n−1 Rn. The label "pseudo" can be further generalized to pseudoscalars and pseudotensors, both of which gain an extra sign flip under improper rotations compared to a true scalar or tensor. (Wikipedia).
The term "tensor" is often misunderstood. Let's figure out what they are through vector examples like velocity, angular momentum, the stress tensor, and the electromagnetic tensor. Brilliant for 20% off: http://brilliant.org/ScienceAsylum ________________________________ VIDEO ANNOTATIONS/
From playlist Gravity as Spacetime Curvature
Using one to one properties to solve an exponential equation
👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo
From playlist Solve Exponential Equations without a Calculator
Using one to one property with different bases to solve an exponential equation
👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo
From playlist Solve Exponential Equations without a Calculator
Given a quadratic function, find the inverse and determine if a function or not
👉 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
Cross product and torque | Moments, torque, and angular momentum | Physics | Khan Academy
The cross product and the direction of torque. Created by Sal Khan. Watch the next lesson: https://www.khanacademy.org/science/physics/oscillatory-motion/harmonic-motion/v/introduction-to-harmonic-motion?utm_source=YT&utm_medium=Desc&utm_campaign=physics Missed the previous lesson? https
From playlist Torque and angular momentum | Physics | Khan Academy
Maxwell's Equations From Differential Forms - 4
In this lesson we discuss why we need to understand the divergence and curl of a 2-form. We discuss why the magnetic field is a "pseudovector" and how to model the magnetic field as a 2-form. Finally we demonstrate how the divergence and curl of a pseudovector can be naturally described in
From playlist QED- Prerequisite Topics
Determining if a equation is a polynomial or not
👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?
some2: transforming normals part 3
Some2 submission version Part1 intro: https://youtu.be/BWr0gQoyUEM Part2: concepts and intuitions: https://youtu.be/QLPcBi47Wzk Part 3: this video This is for Some2. #SoME2 #3b1b All the manim source code will be published soon. License: CC BY-NC-SA 2.0
From playlist Summer of Math Exposition 2 videos
Is it a polynomial with two variables
👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?
Classify a polynomial then determining if it is a polynomial or not
👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?
Learn how to get the same bases to solve an exponential equation
👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo
From playlist Solve Exponential Equations without a Calculator
QED Prerequisites Geometric Algebra 15: Complex Structure
In this lesson we introduce the idea of "complex structure". Complex structure binds scalars with pseudoscalars, vectors with pseudovectors, and bivectors with other bivectors. Please consider supporting this channel on Patreon: https://www.patreon.com/XYLYXYLYX The software I usually u
From playlist QED- Prerequisite Topics
Solving a simple equations with exponents
👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo
From playlist Solve Exponential Equations without a Calculator
Helicity in quantum and classical turbulence experiments by Daniel Lathrop
Turbulence from Angstroms to light years DATE:20 January 2018 to 25 January 2018 VENUE:Ramanujan Lecture Hall, ICTS, Bangalore The study of turbulent fluid flow has always been of immense scientific appeal to engineers, physicists and mathematicians because it plays an important role acr
From playlist Turbulence from Angstroms to light years
Converting an equation to the same base to solve
👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo
From playlist Solve Exponential Equations without a Calculator
Learn how to solve an exponential equation by getting the bases same
👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo
From playlist Solve Exponential Equations without a Calculator
QED Prerequisites 20 Setup For Rotations
In this lesson we focus on some geometric algebra elements that will help us understand how rotations are represented in geometric algebra. We execute some calculations in the *proper* perspective (without basis vectors) and discuss how to create a pseudovector for any plane in any dimensi
From playlist QED- Prerequisite Topics