What Are the Key Differences Between Schmidt Decomposition and SVD?

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Schmidt Decomposition and Singular Value Decomposition (SVD) are both techniques used in linear algebra but serve different purposes. Schmidt Decomposition is specifically applied to bipartite quantum states, allowing for the identification of entanglement properties, while SVD is a more general method used for matrix factorization in various applications. The discussion highlights the importance of understanding the context in which each decomposition is used, particularly in quantum mechanics versus broader mathematical contexts. Additionally, the thread includes a query about applying Schmidt Decomposition to a specific quantum state vector, indicating practical interest in the topic. Understanding these differences is crucial for effectively utilizing each method in relevant fields.
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What's the difference between Schmidt and Single valued decomposition?

https://www.physicsforums.com/showthread.php?t=323859

How could I find it for

<br /> <br /> |\psi&gt;_{AB} = const( |0&gt;_A|0&gt;_B+ |1&gt;_A|1&gt;_B) + const( |0&gt;_A|1&gt;_B+|1&gt;_A|0&gt;_B)<br /> <br />

?
 
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I haven't thought about how to do the Schmidt decomposition of that state vector, but you might find this thread more useful than the one you linked to.
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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