Dark-Alex-17/linear-algebra-theorems-and-definitions
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Finished all chapters and definitions. I need to add subsections and see if there's any theorems or definitions in the appendicies that are worth adding to this as well.

Browse Source
This commit is contained in:
Alex Clarke
2024-02-21 19:31:36 -07:00
parent 85f421fca3
commit 09c5be15d7
45 changed files with 2602 additions and 379 deletions
Download Patch File Download Diff File Expand all files Collapse all files
chapter-0.tex
+8 -8
View File
@@ -14,12 +14,12 @@
& \C & \text{the field of complex numbers} \\
& \C_i & \text{the $i$th Gerschgorin disk} \\
& \cond{A} & \text{the condition number of the matrix $A$} \\
& C^n(\R) & \text{set of functions $f$ on $\R$ with $f^{(n)}$ continuous} \\
& C^\infty & \text{set of functions with derivatives of every order} \\
& C(\R) & \text{the vector space of continuous functions on $\R$} \\
& C([0,1]) & \text{the vector space of continuous functions on $[0,1]$} \\
& C_x & \text{the $T$-cyclic subspaces generated by $x$} \\
& D & \text{the derivative operator on $C^\infty$} \\
& \mathsf{C}^n(\R) & \text{set of functions $f$ on $\R$ with $f^{(n)}$ continuous} \\
& \mathsf{C}^\infty & \text{set of functions with derivatives of every order} \\
& \mathsf{C}(\R) & \text{the vector space of continuous functions on $\R$} \\
& \mathsf{C}([0,1]) & \text{the vector space of continuous functions on $[0,1]$} \\
& \mathsf{C}_x & \text{the $T$-cyclic subspaces generated by $x$} \\
& \mathsf{D} & \text{the derivative operator on $C^\infty$} \\
& \ldet{A} & \text{the determinant of the matrix $A$} \\
& \delta_{ij} & \text{the Kronecker delta} \\
& \ldim{V} & \text{the dimension of $V$} \\
@@ -33,11 +33,11 @@
& F^n & \text{the set of $n$-tuples with entries in a field $\F$} \\
& f(T) & \text{the polynomial $f(x)$ evaluated at the operator $T$} \\
& \mathcal{F}(S,\F) & \text{the set of functions from $S$ to a field $\F$} \\
& H & \text{space of continuous complex functions on $[0, 2\pi]$} \\
& \mathsf{H} & \text{space of continuous complex functions on $[0, 2\pi]$} \\
& I_n \text{ or } I & \text{the $n \times n$ identity matrix} \\
& \Id_V \text{ or } \Id & \text{the identity operator on $V$} \\
& K_\lambda & \text{generalized eigenspace of $T$ corresponding to $\lambda$} \\
& K_\phi & \{x\ |\ (\phi(T))^p(x) = 0 \text{, for some positive integer $p$}\} \\
& K_\phi & \{x : (\phi(T))^p(x) = 0 \text{, for some positive integer $p$}\} \\
& L_A & \text{left-multiplication transformation by matrix $A$} \\
& \lim_{m \to \infty}A_m & \text{the limit of a sequence of matrices} \\
& \linear{V} & \text{the space of linear transformations from $V$ to $V$} \\