What does the notation (<,,>)=<,,> mean?

Question

I came across notation of (<,,>)=<,,>

I'm not sure what "<" mean.

Does it mean: \begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}

Which would transform to:

\begin{bmatrix}0&1&0\\1&0&0\\0&0&1\end{bmatrix}

Answer 1

The "$\langle \, \rangle$" is just the notation for a vector. Though oftentimes you'll see vectors notated with parenthesis "()". Both notations are equally as valid.

The "$T(\cdot)$" denotes some transformation is being applied to the given matrix, which will output a new matrix.

Answer 2

T() is a function T

<x,y,z> is is a variable that consists of a collection of three elements: x, y, z.

“<“ and “>” are set delimiters similar to “{“ and “}”; they are used to describe vectors by their components- as pointed already in the comments, but you may find “[“ and “]” as well when it comes to vectors.

T(<x,y,z>)=<y,x,z> is the analytic expression of the function T. It says that any element of the domain points to an element in the range. In this case, the initial and the transformer vector are symmetric against a plane perpendicular on xy and containing the first bisector of xy.

Now T appears to be the second matrix in your post and has nothing to do with the first, also called the identity matrix.