![]() All the diagonal matrices must be square matrices. Therefore, we were able to show the statement given to us in the question is false. A diagonal matrix does in fact have to be a square matrix. Therefore, just from this definition, we can see that our statement is false. And for this question, the important thing to realize is that all diagonal matrices are square matrices. We recall a diagonal matrix is a square matrix where all of the entries not on the main diagonal of our matrix are equal to zero. So, to answer this question, we’re first going to need to recall exactly what we mean by a diagonal matrix. In other words, this is asking the question, is being a square matrix a requirement for being a diagonal matrix? ![]() The statement says that a diagonal matrix does not have to be a square matrix. So, let’s start by working out exactly what this statement is telling us. And we need to determine whether this statement is true or false. In this question, we’re given a statement. The sum and product of diagonal matrices is again a diagonal matrix. Now lets list a few useful propertiesof diagonal matrices to convince you that they are fairly easy objects. ![]() If you implement these two improvements, the computation executes much quicker.True or false: A diagonal matrix does not have to be a square matrix. In other words, a diagonal matrix is an array whose non-zero entries only appear on the main diagonal. Whenever you see a computation repeated twice, you should consider creating a matrix to hold the intermediate result, such as C = sqrt(d) # B. The expression appears at the beginning of the formula, and the transpose of the expression appears at the end of the formula.
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