linear algebra - Prove that $A^*A + I$ is invertible - Mathematics ...
Let A A be an m × n m × n matrix. Prove that A∗A + I A ∗ A + I is invertible. I'm not sure what to do because everything I try ends up at A∗A A ∗ A again and not AA∗ A A ∗.
matrices - How can we show that $ (I-A)$ is invertible?
You can also argue without using the geometric series. The matrix I − A is invertible if and only if λ = 1 is not an eigenvalue of A. For a contradiction, assume λ = 1 is an eigenvalue. Then Ax = x …
When is $A^TA$ invertible? - Mathematics Stack Exchange
Feb 26, 2023 · Let A be a matrix. What are some necessary/sufficient conditions for the Gram matrix ATA to be invertible? This question came up when I was trying to learn about least …
How to prove that If A is invertible then $A^{-1}$ and $A^2$ are ...
Feb 20, 2016 · a matrix is invertible if and only if its determinat is not null. You can use this fact also: For (b) : Your answer is correct because the determinant is an alternating multilinear …
Inverse vs Invertible - Mathematics Stack Exchange
Dec 11, 2016 · An invertible matrix is one that has an inverse. The inverse itself is a matrix. Note that invertible is an adjective, while inverse (in this sense) is a noun, so they clearly cannot be …
What is the most efficient way to determine if a matrix is invertible?
17 Gauss-Jordan elimination can be used to determine when a matrix is invertible and can be done in polynomial (in fact, cubic) time. The same method (when you apply the opposite row …
Explain proof that any positive definite matrix is invertible
Explain proof that any positive definite matrix is invertible Ask Question Asked 10 years, 6 months ago Modified 3 years, 3 months ago
Is $A + A^{-1}$ always invertible? - Mathematics Stack Exchange
Let A A be an invertible matrix. Then is A +A−1 A + A − 1 invertible for any A A? I have a hunch that it's false, but can't really find a way to prove it. If you give a counterexample, could you …
Is my proof that if - Mathematics Stack Exchange
Oct 4, 2024 · Is my proof that if A A and B B are square matrices and AB A B is invertible, then A A and B B are invertible valid? [duplicate] Ask Question Asked 8 months ago Modified 8 …
matrices - Under what conditions is $AA^T$ invertible?
Feb 17, 2015 · Under what conditions is AAT A A T invertible? Ask Question Asked 10 years, 4 months ago Modified 10 years, 4 months ago