User:Kongrui875/Report5

Problem 1: Proof of exponential of transpose matrix
Report problem 5.1 from.

Find: Prove
Prove ($$)

Solution

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On our honor, we did this assignment on our own, without looking at the solutions in previous semesters or other online solutions.
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The exponential of a matrix is given by

the transpose of a matrix has the following properties ,

Thus,

Thus,

This proved the ($$)

=Reference=

Problem 2: Proof of exponential of diagonal matrix
Report problem 5.2 from.

Given: The formula of exponential of diagonal matrix
A diagonal matrix

where $$\mathbb{C}^{n\times n}$$ represents the set of $$n\times n$$ matrices with complex coefficients

The exponential of the diagonal matrix is given by

Find: Prove
Prove ($$)

Solution

 * {| style="width:100%" border="0"

On our honor, we did this assignment on our own, without looking at the solutions in previous semesters or other online solutions.
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * }

The exponential of a scalar is

The exponential of a matrix is

It is then easy to find out

from ($$),

This proved ($$)