tag:blogger.com,1999:blog-7332477090953898587.post7296561042792325584..comments2022-11-23T03:21:59.265+01:00Comments on IT Shared: The Four Fundamental SubspacesIT Sharedhttp://www.blogger.com/profile/11763288513127086508noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-7332477090953898587.post-70533131706489702832015-06-11T16:57:22.057+02:002015-06-11T16:57:22.057+02:00Thank you very much for the corrections.
Indeed, ...Thank you very much for the corrections.<br /><br />Indeed, if $L(\mathbf x) = A \mathbf x$ is a linear transformation, then the row and null spaces together form the domain for $L$ and the result $L(\mathbf x)$ is always in the column space $C(A)$, so the range of $L$ is the column space $C(A)$.<br /><br />I'm not sure that I'm familiar with the terminology. What do you mean by the "dual space"? The complement? Anonymoushttps://www.blogger.com/profile/03991393318576196455noreply@blogger.comtag:blogger.com,1999:blog-7332477090953898587.post-30614177451506195822015-06-10T21:22:10.355+02:002015-06-10T21:22:10.355+02:00Great post. I think I may have found 2 typos:
for...Great post. I think I may have found 2 typos:<br /><br />for<br /><br />"dimC(A)=dimC(AT)=r,<br />dimN(A)=n−r and<br />dimN(A)=m−r " <--- shouldn't this be dimN(A^T), using the transpose of A?<br /><br />and<br /><br />"The free variable can take any value, for example, we can assign x3=1, so the solution to A=0 is" <--- Ax = 0 with an x in there?<br /><br />Also, couldn't the row and null spaces together be considered the "domain" space of the transformation? similar to the column space being called the image/range space. Could the row and null spaces also be considered a basis for the dual space?<br /><br />Keep up the good work! Anonymoushttps://www.blogger.com/profile/15241850328423660816noreply@blogger.com