vishal007win said:2..
is dis correct!
You didn't answer my question. Here's a slightly different question. What does it mean to say that 3 is an eigenvalue of a matrix A?vishal007win said:it means that no. is the eigen value of new matrix formed by the expression..
A^2010 -2A+3I
Mark44 said:You didn't answer my question. Here's a slightly different question. What does it mean to say that 3 is an eigenvalue of a matrix A?
Mark44 said:I'm looking for an equation that involves A and 3.
No it isn't.temaire said:Also 1x
Mark44 said:No it isn't.
No, A is a matrix, so it can't be equal to any number, and A^2010 - 2A + 3I [itex]\neq[/itex] 2temaire said:So would it be enough to say that since A=1, A^2010 - 2A + 3I = 1 -2 + 3 = 2?
The eigenvalue problem is a mathematical concept that involves finding the eigenvalues (or characteristic values) and corresponding eigenvectors of a square matrix. It is commonly used in various fields such as physics, engineering, and computer science to solve systems of equations and model complex systems.
To solve the eigenvalue problem, you can use various methods such as the characteristic polynomial method, power method, or the QR algorithm. Depending on the complexity of the problem, some methods may be more suitable than others. It is important to understand the underlying concepts and choose the appropriate method for your specific problem.
Eigenvectors and eigenvalues are important in understanding the behavior and properties of a system. Eigenvectors represent the directions in which a linear transformation (represented by a matrix) does not change. Eigenvalues represent the scaling factor by which the eigenvectors are stretched or compressed.
Yes, there are many software programs and calculators that can solve the eigenvalue problem. However, it is still important to have a basic understanding of the concepts and methods involved in order to interpret and verify the results.
The eigenvalue problem has many real-world applications, such as in physics for solving systems of differential equations, in engineering for analyzing vibrations and stability of structures, and in computer science for data compression and image processing. Understanding and being able to solve the eigenvalue problem can help in solving complex problems and making predictions in various fields.