At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions.

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions

Well I guess you answered your own question, haha

Why does \(A=EAE^{-1}\) imply all the diagonal entries are the same?

In fact, what does it mean to right multiply a elementary matrix with two rows switched?

\(E^T=E^{-1}\) for all row switching elementary matrix if that helps.

EAE is equivalent to exchanging row 1 and row 3 then exchange column 1 and column 3 in this case.

Those are the requirements for matrices in the orthogonal group.

How would you end up with 0 ?

Notice that \(i\) and \(j\) are specific rows/columns that are affected by \(E\)

But if \(A_{ii}=A_{jj}=0\) we will certainly have a matrix with 0 on the diagonals right?

i, j are specific two rows that are affected by doing EA.

I should interpret \(A_{ii}=A_{jj}=0\) as \((EA)_{ii}=(EA)_{jj}=0\) right?

I mean exactly that, by doing \(EA\), the diagonal elements in rows \(2,3\) become \(0\)

ofcourse \(i\ne j\)

So the only elements in center of O(n) is \(\pm I\).

looks good to me!