Sylvester Equation appears to be defined as AX+XB=C Unless I am missing something,

Ivor Schofield 2022-02-22 Answered
Sylvester Equation appears to be defined as
AX+XB=C
Unless I am missing something, it looks like one can write it as a simple linear equation
MX=C
Where
M=A+BT
Is this correct? If it is correct, what is the advantage of writing Sylvester Equation in its original form, which naively looks like a more complicated version of the linear equation
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Chettaf04
Answered 2022-02-23 Author has 7 answers

That would be mostly kinda correct if X was assumed symmetric, for then you could turn XB into (BtXt)t=(BtXt)t. You'd still have an extra transpose to get rid of, though, and for that, you'd need to also assume that BtX was symmetric.
So...the two systems are very far from being equivalent. You might want to try this with, say
A=((2  0),(0  1))
B=((1  2),(0  1))
and
C=((3  1),(0  3))
Write out your version of things, solve for X, and plug it into the original: it won't be a solution.

Not exactly what you’re looking for?
Ask My Question
Julien Manning
Answered 2022-02-24 Author has 7 answers
In mathematics, in the field of control theory, a Sylvester equation is a matrix equation of form:[1]
AX+XB=C.
Then given matrices A, B, and C, the problem is to find the possible matrices X that obey this equation. All matrices are assumed to have coefficients in the complex numbers. For the equation to make sense, the matrices must have appropriate sizes, for example they could all be square matrices of the same size. But more generally, A and B must be square matrices of sizes n and m respectively, and then X and C both have n rows and m columns. This should clear things up a bit.
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-06-01

Find the linear approximation of the function f(x)=4x at a=0
Use L(x) to approximate the numbers 3.9 and 3.99 Round to four decimal places

asked 2021-08-15
If a bank pays interest at a rate of i compounded m times a year, then the amount of money Pk at the end of k time periods (where one time period =1mth of a year) satisfies the recurrence relation Pk=[1+im]Pk1 with initial condition P0 = the initial amount deposited. Find an explicit formula for Pn.
asked 2021-09-18
A theater as a seating capacity of 900 and charges $4 for children, $6 for students, and $8 for adults.
At a certain screening with full attendance, there were half as many adults a children and students combined.
The receipts totaled $5600. How many children attended the show?
asked 2021-08-18
Match the function with its name: f(x) = ax + b
a) squaring function
b) square root function
c) cubic function
d) linear function
e) constant function
f) absolute value function
g) greatest integer function
h) reciprocal function
i) identity function
asked 2022-02-25
All solution of AX=0 where A is a n×n matrix and X is a column vector form a subspace of Rn. All the subspaces of Rn are of this type. How to prove this result?
asked 2021-12-09
A quadratic-linear system of equations is graphed below.

a) Use the graph to write the solution to the system. No need to show any work.
b) Write the equation of the linear function drawn on the grid. No need to show any work.
c) Write the equation of the Quadratic function drawn on the grid in standard form. [Hint: use the x-intercepts]
asked 2022-08-05
A path of a toy rocket thrown upward from the ground at a rate of 208 ft/sec is modeled by the quadratic function h(t) = -16t +208t. When will the rocket reach its maximum height? What will be the maximum height?

New questions