Character of Cn Matrix Calculator

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✖Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.ⓘ Theta [θ]

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✖Character of Cn Matrix is the sum of diagonal elements in the character table.ⓘ Character of Cn Matrix [C_n]

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Formula

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Character of Cn Matrix

Formula

`"C"_{"n"} = 2*cos("θ")+1`

Example

`"2.732051"=2*cos("30°")+1`

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Character of Cn Matrix Solution

STEP 0: Pre-Calculation Summary

Formula Used

Character of Cn Matrix = 2*cos(Theta)+1
C_n = 2*cos(θ)+1
This formula uses 1 Functions, 2 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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

C_n = 2*cos(θ)+1 --> 2*cos(0.5235987755982)+1

Evaluating ... ...

C_n = 2.73205080756888

STEP 3: Convert Result to Output's Unit

2.73205080756888 --> No Conversion Required

FINAL ANSWER

2.73205080756888 ≈ 2.732051 <-- Character of Cn Matrix

(Calculation completed in 00.004 seconds)

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Created by Pracheta Trivedi

National Institute Of Technology Warangal (NITW), Warangal

Pracheta Trivedi has created this Calculator and 25+ more calculators!

Verified by Soupayan banerjee

National University of Judicial Science (NUJS), Kolkata

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< 10+ Group Theory Calculators

Probability of Symmetry Species occurring in Reducible Representation

Go 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

Go Angle of Rotation in Cn Axis = 2*pi/Order of Rotation Axis

Order of Rotation Axis in Cn Operation

Go Order of Rotation Axis = (2*pi)/Theta

Character of Cn Matrix

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

Character of Sn Matrix

Go Character of Sn Matrix = 2*cos(Theta)-1

Order of Dnh Point Group

Go Order of Dnh Point Group = 4*Principal Axis

Order of Cnh Point Group

Go Order of Cnh Point Group = 2*Principal Axis

Order of Cnv Point Group

Go Order of Cnv Point Group = 2*Principal Axis

Order of Dnd Point Group

Go Order of Dnd Point Group = 4*Principal Axis

Order of Dn Point Group

Go Order of Dn Point Group = 2*Principal Axis

Character of Cn Matrix Formula

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

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