Sep 28, 2019 · Yes, this is why it is called the identity matrix. Any matrix multiplied by the identity matrix is the original matrix, just as the multiplicative identity for $\mathbb {R}$ is $1$.

Any vector subject to the identity matrix will give you the same vector back. That is the property of the identity matrix. But in light of eigenvectors and eigenvalues, this also matches the situation …

How does adding the identity matrix to a square matrix change the determinant? Ask Question Asked 12 years, 11 months ago Modified 8 months ago

Nov 30, 2018 · 2 Furthermore if you want a concrete example of a matrix whose square is the identity but not itself a simple matrix consider for example this one: $$\begin {bmatrix}\frac {1} …

Every matrix satisfying $A^2=I$ is diagonalizable, because either it is $\pm I$ or its minimal polynomial is $ (x-1) (x+1)$. The general solution is obtained by taking all diagonal matrices …

Mar 11, 2021 · Title says $A$ is the identity matrix. Tht's not the same as $A^TA=E.$

Jun 27, 2019 · If $A$ is a $2 × 2$ complex matrix that is invertible and diagonalizable, and such that $A$ and $A^2$ have the same characteristic polynomial, then $A$ is the $2 × 2$ identity …

Aug 29, 2019 · An identity matrix is in reduced row echelon form. But there are many reduced row echelon matrices that are not an identity matrix, because they have zeros on the diagonal. It’s …

Apr 23, 2016 · Determinant of the Identity Matrix proof Ask Question Asked 9 years, 7 months ago Modified 9 years, 7 months ago

May 16, 2018 · Is there a difference between identity and standard matrices? Or are they are just different notations to distinguish between regular matrices and linear transformations?