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 $1$.

How does adding the identity matrix to a square matrix change the determinant? Ask Question Asked 13 years ago Modified 8 months ago

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 …

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?

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 …

Dec 4, 2013 · Now imagine a matrix that cannot be transformed to the identity matrix using row operations. This means that at some point one cannot choose a pivot in column$~j$ for some …

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 …

May 19, 2024 · Identity matrix for non-square matrices Ask Question Asked 1 year, 6 months ago Modified 1 year, 6 months ago

Oct 23, 2012 · I assumed matrices over $\mathbb {R}$. The connection to other fields is relatively straightforward, though I can elaborate if needed.