description/proof of that positive-definite Hermitian matrix can be transformed to identity by unitary matrix multiplied by positive diagonal matrix from right
Topics
About: matrix
The table of contents of this article
Starting Context
- The reader knows a definition of positive-definite Hermitian matrix.
- The reader knows a definition of unitary matrix.
- The reader knows a definition of orthogonal matrix.
- The reader admits the proposition that any Hermitian matrix can be diagonalized by a unitary matrix to be inevitably real.
Target Context
- The reader will have a description and a proof of the proposition that any positive-definite Hermitian matrix can be transformed to the identity by a unitary matrix multiplied by a positive diagonal matrix from right.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
//
Statements:
//
When
2: Proof
Whole Strategy: Step 1: see that there is a
Step 1:
There is a
As
Step 2:
Let us define