Exchange algorithms | Numerical linear algebra

Pivot element

The pivot or pivot element is the element of a matrix, or an array, which is selected first by an algorithm (e.g. Gaussian elimination, simplex algorithm, etc.), to do certain calculations. In the case of matrix algorithms, a pivot entry is usually required to be at least distinct from zero, and often distant from it; in this case finding this element is called pivoting. Pivoting may be followed by an interchange of rows or columns to bring the pivot to a fixed position and allow the algorithm to proceed successfully, and possibly to reduce round-off error. It is often used for verifying row echelon form. Pivoting might be thought of as swapping or sorting rows or columns in a matrix, and thus it can be represented as multiplication by permutation matrices. However, algorithms rarely move the matrix elements because this would cost too much time; instead, they just keep track of the permutations. Overall, pivoting adds more operations to the computational cost of an algorithm. These additional operations are sometimes necessary for the algorithm to work at all. Other times these additional operations are worthwhile because they add numerical stability to the final result. (Wikipedia).

Video thumbnail

Defining Pi for Physics

Pi is defined as the ratio of the circumference of a circle to its diameter. A frisbee is used to show the definition of pi. The units for pi, radians, are discussed. The conversion factor between revolutions, degrees, and radians is introduced. Want Lecture Notes? http://www.flippingphysi

From playlist IB Physics 6.1: Circular Motion

Video thumbnail

Factorial of a Matrix!

Today, we define the factorial of a matrix using the pi function and power series.

From playlist Linear Algebra

Video thumbnail

PivotPal Guide - My Pivot Layouts and PowerPivot

Sign up for our Excel webinar, times added weekly: https://www.excelcampus.com/blueprint-registration/ http://www.excelcampus.com/pivotpal The My Pivot Layouts feature of PivotPal allows you to save your pivot table options and layout settings, then quickly apply the settings to any pivot

From playlist Power Pivot

Video thumbnail

Introduction to Pivot Tables, Charts, and Dashboards (Part 2)

Sign up for our Excel webinar, times added weekly: https://www.excelcampus.com/blueprint-registration/ http://www.excelcampus.com/charts/pivot-tables-dashboards-part-2 This is part 2 in the series on an introduction to pivot tables and dashboards. In this video I explain some of the diff

From playlist Excel Pivot Tables

Video thumbnail

Find 2 different representations of a point in polar form

Learn how to represent polar points in multiple ways. Recall that angles that are coterminal are exactly the same. So, we can represent polar points in multiple way by representing its coterminal angles. One of the closest coterminal angle to the given angle is the negative angle equivalen

From playlist Rewrite Polar Points in Polar Form #Polar

Video thumbnail

Ex: Simplex Method - Perform the Pivot Operation Given a Tableau

This video explains how to perform the pivot operation when using the simplex method to maximize an objective function. Site: http://mathispower4u.com

From playlist The Simplex Method

Video thumbnail

Example of Linear Independence Using Determinant

Linear Algebra: Let S = {[12, 0, 4, 0], [3,1 , 1, 1], [3, 0, 2, 0], [3, 2, 0, 0]}. Show that S is a linearly independent set by computing the determinant of the matrix whose columns are the vectors in S.

From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics

Video thumbnail

Ex: Simplex Method - Given a Tabeau, Determine the Pivot Column and Pivot Row

This video provides several examples of determining the pivot column and pivot row given a tableau Site: http://mathispower4u.com

From playlist The Simplex Method

Video thumbnail

What is the point on the unit circle for pi

👉 Learn how to find the point on the unit circle given the angle of the point. A unit circle is a circle whose radius is 1. Given an angle in radians, to find the coordinate of points on the unit circle made by the given angle with the x-axis at the center of the unit circle, we plot the a

From playlist Evaluate Trigonometric Functions With The Unit Circle (ALG2)

Video thumbnail

Lecture 4 - Elementary Data Structures

This is Lecture 4 of the CSE373 (Analysis of Algorithms) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1997. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/video-lectures/1997/lecture5.pdf

From playlist CSE373 - Analysis of Algorithms - 1997 SBU

Video thumbnail

A Complete Overview of Quicksort (Data Structures & Algorithms #11)

Here's my introduction to / overview of the quicksort / quick sort algorithm! Patreon: https://csdojo.io/pat The book I mentioned (referral link): https://amzn.to/3j6e6wN My sample code: https://www.csdojo.io/quick 3-way quicksort: https://www.geeksforgeeks.org/3-way-quicksort-dutch-natio

From playlist Data Structures and Algorithms

Video thumbnail

Searching and Sorting Algorithms (part 3 of 4)

Introductory coverage of basic searching and sorting algorithms, as well as a rudimentary overview of Big-O algorithm analysis. Part of a larger series teaching programming at http://codeschool.org

From playlist Searching and Sorting Algorithms

Video thumbnail

2 Ways to Calculate Distinct Count with Pivot Tables

Sign up for our Excel webinar, times added weekly: https://www.excelcampus.com/blueprint-registration/ In this video, you can see two different ways to calculate distinct count in a data set using Pivot Tables. These are two solutions to a Data Analysis Challenge that I gave to viewers. Y

From playlist Pivot Tables

Related pages

Absolute value | Matrix multiplication | Reduced row echelon form | Gaussian elimination | Row echelon form | Matrix (mathematics) | Numerical stability | Permutation matrix | Algorithm | Simplex algorithm | Quicksort