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3 cards from this section. Quick, good the night before a test.
Define a diagonal matrix in your own words.
Consider where the non-zero elements can be located.
If a diagonal matrix has three non-zero elements, what is its rank?
Remember, rank is about counting non-zero diagonal elements.
What is the rank of the diagonal matrix D = [[3, 0, 0], [0, 4, 0], [0, 0, 0]]?
Count the non-zero elements on the diagonal.
True or False: A zero matrix is considered a diagonal matrix.
Reflect on the definition of diagonal matrices.
Given the diagonal matrix D = [[7, 0, 0], [0, 5, 0], [0, 0, -3]], calculate the rank and explain your method.
Refer to how many diagonal entries you see that are non-zero.
If you manipulate a diagonal matrix by setting one of its non-zero diagonal entries to zero, how would that change its rank? Provide an example.
Think about how rank is determined by counting non-zeros.
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