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How can we show that $ (I-A)$ is invertible? Ask Question Asked 13 years, 9 months ago Modified 6 years, 11 months ago

If $A$, $B$ are square matrices and $I-AB$ is invertible how do I prove that $I-BA$ is invertible? This is exercise 8 of section 6.2 in Linear Algebra by Hoffman and Kunze.

Prove that $A+I$ is invertible if $A$ is nilpotent [duplicate] Ask Question Asked 13 years, 6 months ago Modified 5 years, 10 months ago

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 synonymous.

Jul 31, 2017 · Now $AB$ invertible means $u\circ v$ is an automorphism of $K^n$, so $u$ is surjective and $v$ is injective. As we're in finite dimension, this means $u$ and $v$ are …

Feb 17, 2015 · Under what conditions is $AA^T$ invertible? Ask Question Asked 10 years, 9 months ago Modified 10 years, 9 months ago

Which is a different way of saying that $X$ has a left inverse. Actually, if $X^TX$ is invertible, then $ (X^TX)^ {-1}X^T$ is a left inverse of $X$ and is exactly the Moore-Penrose pseudoinverse of …

Sep 25, 2015 · A function is invertible if and only if it is bijective (i.e. both injective and surjective). Injectivity is a necessary condition for invertibility but not sufficient.

Mar 30, 2013 · That a matrix is invertible means the map it represents is invertible, which means it is an isomorphism between linear spaces, and we know this is possible iff the linear spaces' …