Prove that for a real matrix $A$, $\ker (A) = \ker (A^TA)$ You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do I get it? Instead, you can save this post to reference later
$\ker (A^TA) = \ker (A)$ - Mathematics Stack Exchange I am sorry i really had no clue which title to choose I thought about that matrix multiplication and since it does not change the result it is idempotent? Please suggest a better one
linear algebra - Prove that $\ker (AB) = \ker (A) + \ker (B . . . You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do I get it? Instead, you can save this post to reference later
Can $RanA=KerA^T$ for a real matrix $A$? And for complex $A$? You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do I get it? Instead, you can save this post to reference later
How to find $ker (A)$ - Mathematics Stack Exchange You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do I get it? Instead, you can save this post to reference later
If Ker (A)=$\ {\vec {0}\}$ and Ker (B)=$\ {\vec {0}\}$ Ker (AB)=? Thank you Arturo (and everyone else) I managed to work out this solution after completing the assigned readings actually, it makes sense and was pretty obvious Could you please comment on "Also, while I know that Ker (A)=Ker (rref (A)) for any matrix A, I am not sure if I can say that Ker (rref (A) * rref (B))=Ker (AB) Is this statement true?" just out of my curiosity?
How to find a basis of an image of a linear transformation? It is $$ kerA = (1,1,1) $$ But how can I find the basis of the image? What I have found so far is that I need to complement a basis of a kernel up to a basis of an original space But I do not have an idea of how to do this correctly I thought that I can use any two linear independent vectors for this purpose, like $$ imA = \ { (1,0,0), (0,1,0
How to find basis of ker (A)? - Mathematics Stack Exchange You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do I get it? Instead, you can save this post to reference later