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I was told in my advanced linear algebra class that $$\partial_t I = 0$$ but i do not see how. I’m not too familiar with matrix calculus but i get that $I$ doesn’t change as $t$ changes but how do you differentiate a matrix? Shouldn’t it be the 0 vector or 0 matrix? How is it a scalar?

John D
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  • It is impossible for you to solve the exercise if you don't know how to differentiate a matrix. What definition does your book/lecture notes give? – Richard Jensen Sep 09 '21 at 07:02
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    $$ \partial_t I = \lim_{h\to 0} \frac{I(t+h) - I(t)}{h} = \lim_{h\to 0} \frac{I - I}{h} = 0 $$ The zero matrix of the same dimensions – Physor Sep 09 '21 at 07:23
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    Matrices do not have derivatives. Functions and mappings have derivatives. You can view a matrix as a representation of a linear mapping, in which case the matrix is also the derivative of that same mapping. Or maybe you have a matrix function, in which case the derivative is $0$ because the function is constant. – 5xum Sep 09 '21 at 07:23
  • @RichardJensen We use the Boyd optimization book which doesn’t mention it. This is an intro graduate class so the professor said that he expects us to learn the matrix calculus from wikipedia as we go along :( – John D Sep 09 '21 at 07:30
  • @Physor Ah i asked my Professor and he said it was a mistake saying 0 was a scalar. Turns out he meant the 0 matrix, youre answer makes a lot of sense! I will probably close this question since it is unlikely to be of use to others – John D Sep 09 '21 at 07:37

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