Why is the 2-norm of A^k equal to 2-norm of T^k?

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In summary, The conversation discusses the Schur decomposition of matrix A into Q^H * A * Q = T = D + N, where D is a diagonal matrix with eigenvalues of A and N is a strictly upper triangular matrix. It is used in a proof that states ||A^k|| 2 norm = ||T^k|| 2 norm for k>=0. However, the person does not understand why this equality is true and attempts to work it out with an example.
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vabamyyr
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Let Q^H * A * Q = T = D + N be Schur decomposition of A. D is a diagonal matrix with eigenvalues of A and N is strictly upper triangular matrix. This sentence is used in a proof which I am not going to state but at some point it states that ||A^k|| 2 norm = ||T^k|| 2 norm for k>=0. I don't understand
where this equality comes from. I tried to work this equality out with an example of taking
 
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You can help yourself, and us, by using the latex formatting in this forum to make it clear what it is you're asking. Note the text in the reply box is not formatted literally.
 
  • #3
The problem is simple: why is the 2-norm of A^k equal to 2-norm of T^k?
 

FAQ: Why is the 2-norm of A^k equal to 2-norm of T^k?

What is algebra?

Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols to solve equations and express relationships between quantities.

What are the basic operations in algebra?

The basic operations in algebra are addition, subtraction, multiplication, division, and exponentiation. These operations are used to manipulate equations and solve for unknown variables.

What is the order of operations in algebra?

The order of operations in algebra is a set of rules that determines the order in which operations should be performed in an expression. The acronym PEMDAS is commonly used to remember the order: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

How do I solve a basic algebra problem?

To solve a basic algebra problem, you need to follow the order of operations to simplify the expression and isolate the variable on one side of the equation. Then, you can use inverse operations to solve for the variable.

Why is algebra important?

Algebra is important because it helps us understand and describe relationships between quantities in the real world. It is also used in many fields such as science, engineering, and economics to solve complex problems and make predictions.

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