Matrices with hyperbolic functions

In summary, the conversation is about finding a solution for an equation involving the matrices A and M. The person has found that A^2 equals the identity matrix, but is unsure how to incorporate that into the equation to get sinh and cosh in the expression. Another person suggests looking up the Taylor series of sinh and cosh and comparing them with the infinite series obtained using A^2=I. The first person thanks the second person and says they now understand.
  • #1
samjohnny
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1

Homework Statement



I thought it would be better to attach it.

Homework Equations





The Attempt at a Solution



So for the first part I've found that A^2=the Identity matrix, but from there I don't have much of an idea on how to substitute that into the equation for M and end up with sinh and cosh in my expression. Please help
 

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  • #2
samjohnny said:

Homework Statement



I thought it would be better to attach it.

Homework Equations





The Attempt at a Solution



So for the first part I've found that A^2=the Identity matrix, but from there I don't have much of an idea on how to substitute that into the equation for M and end up with sinh and cosh in my expression. Please help

Look up the taylor series of sinh and cosh and compare them with the infinite series you get using that A^2=I.
 
  • #3
Dick said:
Look up the taylor series of sinh and cosh and compare them with the infinite series you get using that A^2=I.

Thanks I've got it now! :)
 

FAQ: Matrices with hyperbolic functions

1. What are matrices with hyperbolic functions?

Matrices with hyperbolic functions are matrices that contain entries that are hyperbolic functions, such as sinh, cosh, and tanh. These functions are commonly used in mathematics and physics to model various physical phenomena.

2. What are the properties of matrices with hyperbolic functions?

Matrices with hyperbolic functions have similar properties to regular matrices, such as addition, subtraction, and multiplication. However, they also have unique properties related to the hyperbolic functions, such as the hyperbolic cosine squared identity and the hyperbolic sine and cosine addition formulas.

3. How are matrices with hyperbolic functions used in real-world applications?

Matrices with hyperbolic functions are commonly used in physics and engineering to model and analyze systems with non-linear behaviors. They can also be used in data analysis and machine learning to represent complex relationships between variables.

4. Are there any special techniques for solving matrices with hyperbolic functions?

Yes, there are special techniques for solving matrices with hyperbolic functions, such as using the hyperbolic functions addition formulas and manipulating the matrices to simplify the equations. In some cases, numerical methods may also be used to solve these matrices.

5. What are some common mistakes when working with matrices with hyperbolic functions?

Some common mistakes when working with matrices with hyperbolic functions include forgetting to use the hyperbolic functions addition formulas, not simplifying the equations enough, and not being familiar with the properties of hyperbolic functions. It is important to carefully follow the rules and properties of these functions when working with matrices that contain them.

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