A bad Cayley–Hamilton theorem proof Given $A\in M_{n \times n}(\mathbb{F})$ and $p_{A}(x)=\det(xI-A)$ why saying that $\det(AI-A)=0$ is not valid?
To prove Cayley-Hamilton theorem, why can't we substitute $A$ for $\lambda$ in $p(\lambda) = \det(\lambda I - A)$? Cayley Hamilton Theorem states that if $A$ is an $n \times n$ matrix over the field $F$ then $p(A) = 0$.  We note that $p(\lambda) = \det(\lambda I - A)$. Hence, why can't we just substitute $\lambda$ with $A$ and directly prove Cayley-Hamilton Theorem by saying that $p(A) = p(\lambda) = \det(\lambda I - A) = \det(AI - A) = 0$?
Over the past couple of days there have been a few questions about overlapping proposals and questions that could belong on multiple sites:        What is the best practice before / after asking a question if you think your question might be better on another site?  or  If I think my question might belong on multiple sites as per the above posts? Connect Talend to Salesforce using OAuth JWT Flow I followed the steps exactly mentioned here  for connecting Talend to salesforce.  I have done the configuration in Talend and added the test(sandbox) URL in the advanced setting. I am facing an error while trying to establish the Oauth connection (JWT) between Talend ETL tool and salesforce: {'error':'invalid_grant','error_description':'invalid assertion'} Here is the screenshot of the configuration and error message:   Please help to resolve this issue. What is the difference between <%# and <%= in ASP.NET MVC? Finding an Inverse Function and Composition of Functions? 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To put it simply:  The spontanously breaking of what is attributed to Higgs mechanism?   local gauge symmetry global symmetry, since breaking of a "gauge symmetry" should not have any effect on physics. In higgs mechanism, the really broken symmetry is a global one. Mathematically, it is similar in looking as fixing a gauge, but one should not think it as a spontanously breakdown of local gauge symmetry. other.   Is SSB really indispensable for Higgs mechanism?    yes, Higgs mechanism is relied on the SSB of some symmetry (above question), the other approches of description eventually has spontanously broke some symmetry. 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Indeed, as already shown by Higgs and Kibble, the   mechanism can be explained in terms of gauge invariant variables,   without invoking spontaneous symmetry breaking     In the introduction it says:      In particular, we emphasize that global U(1) phase rotation symmetry,   and not gauge symmetry, is spontaneously violated, and show that the   BCS wave function is, contrary to claims in the literature, fully   gauge invariant It is discouraged to simply catch System.Exception. Instead, only the &quot;known&quot; exceptions should be caught. Now, this sometimes leads to unnecessary repetitive code, for example: try {     WebId = new Guid(queryString[&quot;web&quot;]); } catch (FormatException) {     WebId = Guid.Empty; } catch (OverflowException) {     WebId = Guid.Empty; }  I wonder: Is there a way to catch both exceptions and only call the WebId = Guid.Empty call once? The given example is rather simple, as it's only a . 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