My lecture notes write that two matrices are said to be similar if there exists an n × n invertible matrix P such that B = P − 1 A P.
This is essentially because for such small matrices the characteristic polynomial leaves very little room for variation of the minimal polynomial (and other invariant factors that
Determine mathematic problems
Math is a way of determining the relationships between numbers, shapes, and other mathematical objects.
Clarify math problem
Math is a way of solving problems using numbers and equations
Fast answers
If you need a quick answer, ask a librarian!
Do math equations
I love solving math equations! There's something so satisfying about finding the right answer and knowing that it's all correct.
If matrices A and B are similar, matrix B can be found by applying elementary operations on the rows of matrix A, and vice versa. Obviously, the similarity between matrices is a reflective operation. That is, if A is similar to B, B is also similar to A. Furthermore, the similarity of matrices is also symmetric. See more
Similar matrices represent the same linear operator with respect to different bases (this is the motivation for the notion of similarity), and so naturally such matrices must have
matrix A. So, both A and B are similar to A, and therefore A is similar to B. However, if two matrices have the same repeated eigenvalues they may not be distinct. For example, the zero
Solve math
Solving math equations can be challenging, but it's also a great way to improve your problem-solving skills.
Have more time for your pursuits
If you want more time for your pursuits, consider hiring a virtual assistant.
Get assistance
If you're struggling to complete your assignments, Get Assignment can help. We offer a wide range of services to help you get the grades you need.
