Symmetric And Skew Symmetric Matrices
Chapter Name : Matrices |
Sub Topic Code : 104_12_03_06_01 |
Topic Name : Symmetric And Skew Symmetric Matrices |
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Sub Topic Name : Symmetric And Skew Symmetric Matrices |
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Introduction
A symmetric matrix is a matrix which is equal to its transpose; a skew symmetric matrix is a matrix which is equal to the negative of its transpose.
Pre-Requisites:
Order of Matrix, square matrices, transpose of matrix
Activity:
Observe how the diagonal elements of skew symmetric matrices are 0.
Real Life Question:
Can you come up with an instance of a symmetric matrix data set?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Order of matrix | The number of rows and columns in the matrix; m (rows) x n (columns). |
| Square matrix | A square matrix is a matrix where the number of rows is equal to the number of columns. |
| Diagonal elements | Diagonal elements of a matrix are elements like x11, x22, x33. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Dice | Using Dice one can replicate a matrix format. Place dice in a manner that it would show a 2x2 format. For representing 0, remove the die. |
Real life uses :
Prices and number of units sold can be fit into such matrices.
Practical examples around us
| Examples | Explainations |
|---|---|
| Use in calculations | Symmetric matrices can be used to calculate data where the order of rows and columns are not restrictive. |
What you learn in Theory:
Basics about symmetric and skew symmetric matrices.
What you learn in Practice:
Every square matrix can be expressed as a sum of symmetric and skew symmetric matrices.