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## Main Question or Discussion Point

I am working through linear algebra from MITs MOOC online courses. One of the question refers to the uncertainty principle. It states:

AB-BA=I can happen for infinite matrices with A

My question is how does

[tex]x^{ T }x=x^{ T }ABx-x^{ T }BAx [/tex]?

AB-BA=I can happen for infinite matrices with A

**[tex]A=A^{ T }\\ and\\ B=-B^{ T }\\ Then\\ x^{ T }x=x^{ T }ABx-x^{ T }BAx\le 2\parallel Ax\parallel \parallel Bx\parallel[/tex]**

My question is how does

[tex]x^{ T }x=x^{ T }ABx-x^{ T }BAx [/tex]?