linear algebra - Do Diagonal Matrices Always Commute?
2016年3月15日 · $\begingroup$ When the diagonal matrix is on the right, it scales the columns of the matrix it is multiplying. when the diagonal matrix is on the left, it scales the rows. Since column-scaling and row scaling are different operations, there are only very limited circumstances that the matrices will commute. $\endgroup$ –
How to prove that the normalizer of diagonal matrices in
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Diagonalizable matrices with complex values are dense in set of
Part 2: The set of upper triangular matrices with distinct diagonal entries is dense in the set of upper triangular matrices... $\endgroup$ – N. S. Commented Feb 11, 2012 at 1:00
linear algebra - Basis for the set of diagonal matrices
2017年12月15日 · Let A be the set of all diagonal matrices. How can we calculate it's basis and dimension? I am not really good at it. Can you help me with this, so thus I will have some picture.
Prove that $AB=BA$ if $A, B$ are diagonal matrices
$\begingroup$ The proof is OK but it would be good to prove first that the product of two diagonal matrices is the diagonla matrix obtained by multiplying the elements of the diagonal. Once this done, the result is clear, and you will need this so often after... $\endgroup$
Prove that the set of all the diagonal matrices is a vector space
Once you have proved that a scalar multiple of a diagonal matrix, as well as the sum of two diagonal matrices is again a diagonal matrix, and finally that the zero matrix is a diagonal matrix, you have proved that the diagonal matrices are a sub-vector space of the space of all matrices.
What is the dimension of the vector space of all diagonal $n …
2013年11月30日 · In general, what is the dimension of the vector space of all n x n diagonal matrices? and Thank you. $\endgroup$ – user112430 Commented Nov 30, 2013 at 11:13
linear algebra - How is diagonal matrices a subspace of upper ...
The collection of all matrices which are $0$ off diagonal, and have all diagonal terms equal is a subspace of the space of all matrices. Maybe that will take care of part of your objection. Maybe that will take care of part of your objection.
linear algebra - When is matrix multiplication commutative ...
There are lots of "special cases" that commute. The multiplication of two diagonal matrices, for example. Aside: for any two square invertible matrices, A, B, there is something that can be said about AB vs. BA. If AB = C then BA = inv(A) C A = B C inv(B) (Proof: substitute AB for C in the result, and cancel inverses)
Standard Notation for diagonal matrices - Mathematics Stack …
2016年2月17日 · One common way (among others) to specify the set of non-negative reals is $\mathbb{R}_{\ge 0}$. Thus, $\mathbb{R}_{\ge 0}^n$ would be the corresponding Cartesian product (i.e. the set of all nonnegative n-tuples). A standard way to talk about diagonal matrices uses $\text{diag}(\cdot)$ which maps an n-tuple to the corresponding diagonal matrix: