## Character of Cn Matrix Solution

STEP 0: Pre-Calculation Summary
Formula Used
Character of Cn Matrix = 2*cos(Theta)+1
Cn = 2*cos(θ)+1
This formula uses 1 Functions, 2 Variables
Functions Used
cos - Trigonometric cosine function, cos(Angle)
Variables Used
Character of Cn Matrix - Character of Cn Matrix is the sum of diagonal elements in the character table.
Theta - (Measured in Radian) - Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.
STEP 1: Convert Input(s) to Base Unit
Theta: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Cn = 2*cos(θ)+1 --> 2*cos(0.5235987755982)+1
Evaluating ... ...
Cn = 2.73205080756888
STEP 3: Convert Result to Output's Unit
2.73205080756888 --> No Conversion Required
2.73205080756888 2.732051 <-- Character of Cn Matrix
(Calculation completed in 00.002 seconds)
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## Credits

Created by Pracheta Trivedi
National Institute Of Technology Warangal (NITW), Warangal
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National University of Judicial Science (NUJS), Kolkata
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## < 10+ Group Theory Calculators

Probability of Symmetry Species occurring in Reducible Representation
No. of Times Irrep occurs in Reducible = 1/Order of Group*add(Character of Reducible Representation+Character of Irreducible Representation+Number of Symmetry Operation)
Angle of Rotation in Cn Axis
Angle of Rotation in Cn Axis = 2*pi/Order of Rotation Axis
Order of Rotation Axis in Cn Operation
Order of Rotation Axis = (2*pi)/Theta
Character of Cn Matrix
Character of Cn Matrix = 2*cos(Theta)+1
Character of Sn Matrix
Character of Sn Matrix = 2*cos(Theta)-1
Order of Dnh Point Group
Order of Dnh Point Group = 4*Principal Axis
Order of Cnh Point Group
Order of Cnh Point Group = 2*Principal Axis
Order of Cnv Point Group
Order of Cnv Point Group = 2*Principal Axis
Order of Dnd Point Group
Order of Dnd Point Group = 4*Principal Axis
Order of Dn Point Group
Order of Dn Point Group = 2*Principal Axis

## Character of Cn Matrix Formula

Character of Cn Matrix = 2*cos(Theta)+1
Cn = 2*cos(θ)+1

## What are Characters of Cn in Character Table?

A character table is a 2 dimensional chart associated with a point group that contains the irreducible representations of each point group along with their corresponding matrix characters.For Cn, generate a character table with a trivial A representation, an alternating B representation if n is even, and an appropriate number of E representations. The E1 has characters equal to the double cosine of the respective rotation, 2cosφ, the E2 has 2cos2φ etc.

## How to Calculate Character of Cn Matrix?

Character of Cn Matrix calculator uses Character of Cn Matrix = 2*cos(Theta)+1 to calculate the Character of Cn Matrix, Character of Cn Matrix is the sum of diagonal elements in the Character Table. It is also called a trace. The trace of a matrix remains unchanged upon a unitary coordinate transformation. Character of Cn Matrix is denoted by Cn symbol.

How to calculate Character of Cn Matrix using this online calculator? To use this online calculator for Character of Cn Matrix, enter Theta (θ) and hit the calculate button. Here is how the Character of Cn Matrix calculation can be explained with given input values -> 2.732051 = 2*cos(0.5235987755982)+1.

### FAQ

What is Character of Cn Matrix?
Character of Cn Matrix is the sum of diagonal elements in the Character Table. It is also called a trace. The trace of a matrix remains unchanged upon a unitary coordinate transformation and is represented as Cn = 2*cos(θ)+1 or Character of Cn Matrix = 2*cos(Theta)+1. Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.
How to calculate Character of Cn Matrix?
Character of Cn Matrix is the sum of diagonal elements in the Character Table. It is also called a trace. The trace of a matrix remains unchanged upon a unitary coordinate transformation is calculated using Character of Cn Matrix = 2*cos(Theta)+1. To calculate Character of Cn Matrix, you need Theta (θ). With our tool, you need to enter the respective value for Theta and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well. Let Others Know