How can I ensure that Q'*M*Q=I without using MATLAB?

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SUMMARY

The discussion focuses on ensuring that the equation Q'*M*Q=I holds true, where Q represents the matrix of eigenvectors, M is the mass matrix, and I is the identity matrix. The participant seeks a solution without utilizing MATLAB and questions the conditions under which a diagonal matrix can be achieved. It is established that diagonalization is not always possible, and the Jordan Normal form is suggested as a relevant concept for further understanding.

PREREQUISITES
  • Understanding of eigenvalues and eigenvectors
  • Familiarity with matrix diagonalization
  • Knowledge of mass and stiffness matrices in mechanical systems
  • Basic concepts of Jordan Normal form
NEXT STEPS
  • Research the properties of eigenvectors and their role in matrix transformations
  • Study the conditions for diagonalization of matrices
  • Explore the Jordan Normal form and its applications in linear algebra
  • Investigate alternative numerical methods for matrix operations without MATLAB
USEFUL FOR

Students and professionals in engineering, particularly those studying dynamics and linear algebra, as well as anyone interested in matrix theory and its applications in mechanical systems.

nellierd
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Homework Statement


det(K-lambdaM)=0

K is stiffness and M is mass matrix

Homework Equations



How do I make sure that Q'*M*Q=I
Where Q is the matrix whose column entries are the eigen vectors.

The Attempt at a Solution



I want to know how to do it without MATLAB help. Is it always true that I will get a diagonal matrix?
 
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