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--- math54-f22:midterm_2 [2022/11/03 16:59]
pzhou created
+++ math54-f22:midterm_2 [2022/11/03 17:04] (current)
pzhou
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   * Concretely, if one is given $A x = b$ with numbers, how to solve it?
   * What is LPU decomposition?
-  * What is a complete flag in $K^n$?
+  * What is a complete flag in $K^n$? How does a linear transformation acts on a flag?
+  * What's Inertia theorem about? (find a basis so that a quadratic form looks simple).
+  * What is the difference between classifying a complex symmetric form, and a real symmetric form?
+  * What is the difference between a Hermitian sesquilinear form and a symmetric bilinear form?
+  * What does 'diagonalization' mean? (find a nice basis, so the matrix form of whatever object one look at is a diagonal matrix)
+  * Eigenvalues: when can you diagonalize, and when you cannot diagonalize? (check matrix to see if it is normal)
+  *

Lecture Notes