figuring out orthonormal basis for a matrix?
up vote
0
down vote
favorite
For $T in mathcal{L}(mathbb{R}^2)$ given by $T(x,y) = (x, -y)$, its basis is $ mathcal{M}(T) = begin{pmatrix}1 & 0\0 & -1end{pmatrix}$. How would I find the orthonormal basis for this? Is $frac{1}{sqrt{2}}(x + y), frac{1}{sqrt{2}}(x - y)$ one? How would I figure this out?
linear-algebra
New contributor
add a comment |
up vote
0
down vote
favorite
For $T in mathcal{L}(mathbb{R}^2)$ given by $T(x,y) = (x, -y)$, its basis is $ mathcal{M}(T) = begin{pmatrix}1 & 0\0 & -1end{pmatrix}$. How would I find the orthonormal basis for this? Is $frac{1}{sqrt{2}}(x + y), frac{1}{sqrt{2}}(x - y)$ one? How would I figure this out?
linear-algebra
New contributor
It is the usual basis ${(1,0), (0,1)}$.
– Kavi Rama Murthy
Nov 15 at 6:20
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
For $T in mathcal{L}(mathbb{R}^2)$ given by $T(x,y) = (x, -y)$, its basis is $ mathcal{M}(T) = begin{pmatrix}1 & 0\0 & -1end{pmatrix}$. How would I find the orthonormal basis for this? Is $frac{1}{sqrt{2}}(x + y), frac{1}{sqrt{2}}(x - y)$ one? How would I figure this out?
linear-algebra
New contributor
For $T in mathcal{L}(mathbb{R}^2)$ given by $T(x,y) = (x, -y)$, its basis is $ mathcal{M}(T) = begin{pmatrix}1 & 0\0 & -1end{pmatrix}$. How would I find the orthonormal basis for this? Is $frac{1}{sqrt{2}}(x + y), frac{1}{sqrt{2}}(x - y)$ one? How would I figure this out?
linear-algebra
linear-algebra
New contributor
New contributor
New contributor
asked Nov 15 at 6:14
user589759
111
111
New contributor
New contributor
It is the usual basis ${(1,0), (0,1)}$.
– Kavi Rama Murthy
Nov 15 at 6:20
add a comment |
It is the usual basis ${(1,0), (0,1)}$.
– Kavi Rama Murthy
Nov 15 at 6:20
It is the usual basis ${(1,0), (0,1)}$.
– Kavi Rama Murthy
Nov 15 at 6:20
It is the usual basis ${(1,0), (0,1)}$.
– Kavi Rama Murthy
Nov 15 at 6:20
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
user589759 is a new contributor. Be nice, and check out our Code of Conduct.
user589759 is a new contributor. Be nice, and check out our Code of Conduct.
user589759 is a new contributor. Be nice, and check out our Code of Conduct.
user589759 is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2999306%2ffiguring-out-orthonormal-basis-for-a-matrix%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
It is the usual basis ${(1,0), (0,1)}$.
– Kavi Rama Murthy
Nov 15 at 6:20