Consider the set of all complex numbers. This can be considered a vector space, because it satisfies the ten defining properties. We can also define an inner product for this vector space where is the real part of and Im( ) is the imaginary part of . This leads to the following definition for norm i. Consider the following basis set for the vector space described above: Using the Gram-Schmidt method, find an orthogonal basis set.ii. Using your orthogonal basis set from part i., find vector expansions for This will allow you to write iii. We now want to represent the vector using the basis set Use reciprocal basis vectors to find the expansion for in terms of the basis vectors This will allow you to write as a new column of numbers x”.iv. Show that the representations for that you found in parts ii. and iii. are equivalent (the two columns of numbers x and x” both represent the same vector
Consider the set of all complex numbers. This can be considered a vector space, because it…
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