Chardonnay Felix

2021-01-31

Find a basis for the space of $2\times 2$ diagonal matrices.

$\text{Basis}=\{\left[\begin{array}{cc}& \\ & \end{array}\right],\left[\begin{array}{cc}& \\ & \end{array}\right]\}$

Jayden-James Duffy

Skilled2021-02-01Added 91 answers

Step 1

let the space of$2\times 2$ diagonal matrices be as

$\left[\begin{array}{cc}a& 0\\ 0& b\end{array}\right]$

we can choose values of a and b randomly Step 2

Basis of matrix$\left[\begin{array}{cc}a& 0\\ 0& b\end{array}\right]$ can be taken as

a=1,b=0

$\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}\right]$

a=0, b=1$\left[\begin{array}{cc}0& 0\\ 0& 1\end{array}\right]$

$\text{Basis}=\{\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}\right],\left[\begin{array}{cc}0& 0\\ 0& 1\end{array}\right]\}$

let the space of

we can choose values of a and b randomly Step 2

Basis of matrix

a=1,b=0

a=0, b=1

Don Sumner

Skilled2023-05-09Added 184 answers

karton

Expert2023-05-09Added 613 answers

user_27qwe

Skilled2023-05-09Added 375 answers

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