What is the Significance of the Lambda Symbol in Transformation Matrices?

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The lambda symbol \Lambda_{\nu}^{\mu} is primarily associated with the Lorentz transformation matrix, though its use can vary by author. Enclosing it in brackets \left(\Lambda_{\nu}^{\mu}\right) is recommended to clarify that it refers to the entire matrix rather than a specific component. The notation (\Lambda^\mu{}_\nu) is less favored by some, who prefer simply using \Lambda for simplicity. The positioning of indices is crucial in most texts, as it conveys important information about the matrix structure. Clarity in notation is essential to avoid misunderstandings in mathematical discussions.
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Does the lambda symbol \Lambda_{\nu}^{\mu} refer specifically to the Lorentz transformation matrix or to any transformation matrix?
Also, is it essential that it's enclosed in brackets \left(\Lambda_{\nu}^{\mu}\right)
to indicate the entire matrix and not a particular component? Does it matter that much or is it an obvious faux pas?
Thank you
 
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I think it's usually just the components of a Lorentz transformation, but you shouldn't assume that every author uses that convention.

I'm not a fan of the (\Lambda^\mu{}_\nu) notation. I assume it denotes the matrix with \Lambda^\mu{}_\nu on row \mu, column \nu? I would just write \Lambda.

Note that in most books, the horizontal positioning of the indices is important.
 
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