commit f34939dba033645cad998cbf3e1dd8d361922c62
parent 6feb9c7f0940d1bce3493c73a4cff03f834844f1
Author: Andrew <andrewlaack1@gmail.com>
Date: Mon, 12 Aug 2024 22:49:04 -0500
Took notes, ending day
Diffstat:
12 files changed, 91 insertions(+), 1 deletion(-)
diff --git a/Connectives.md b/Connectives.md
@@ -0,0 +1,15 @@
+:discrete:
+# Connectives
+
+1.1.1
+
+## Notes
+
+**Definition:** Connectives are necessary for the creation of compound propositions and they are the following:
+
+- Negation (not | $\neg$)
+- Conjunction (and | $\wedge$)
+- Disjunction (or | $\vee$)
+- Implication (If, then | $\to$)
+- Biconditional (If and only if | $\iff$)
+- Exclusive or ($\oplus$)
diff --git a/CramersRule.md b/CramersRule.md
@@ -0,0 +1,12 @@
+:lin-alg:
+# Cramer's Rule
+
+3B1B
+
+## Notes
+
+**Definition:** Cramer's rule is an alternative to [[GaussianElimination.md]] for solving systems of equations.
+
+While slower and generally worse, it is novel.
+
+I don't really understand how this works.
diff --git a/DiscreteMath.md b/DiscreteMath.md
@@ -0,0 +1,13 @@
+:index: :discrete:
+# Discrete Math
+
+Discrete math related links.
+
+## Links
+
+#### Discrete Mathematics and Its Applications
+
+Unit 1.1:
+ - [[Proposition.md]]
+ - [[Negation.md]]
+ - [[Connectives.md]]
diff --git a/Duality.md b/Duality.md
@@ -0,0 +1,10 @@
+:lin-alg:
+# Duality
+
+3B1B
+
+## Notes
+
+**Definition:** Duality is a natural but surprising correspondence between two types of things.
+
+This is like finding out that the dot product can be used to find the projection of a vector onto another vector.
diff --git a/EigenVector.md b/EigenVector.md
@@ -1,4 +1,4 @@
-:ml: :cs331:
+:ml: :cs331: :lin-alg:
# Eigen Vector
Self Study
@@ -8,3 +8,5 @@ Self Study
**Definition:** An Eigen Vector is a non-zero vector that when a linear transformation is performed upon it, the resulting vector is only moved by a scalar multiple (remains on the same line).
Associated with this, we also have an Eigen value which is the amount that a point on the Eigen Vector is distorted by (multiplied by this scalar)
+
+This can be thought of as the axis of rotation when in R^3. Additionally, we know the eigen value is 1 in a rotation as there is no stretching.
diff --git a/GaussianElimination.md b/GaussianElimination.md
@@ -0,0 +1,12 @@
+:lin-alg:
+# Gaussian Elimination (row reduction)
+
+Khan U1
+
+## Notes
+
+**Definition:** Gaussian elimination is the process of simplifying a system of equations to [[ReducedRowEchelonForm.md]] to solve the system.
+
+Basically, we perform row operations on an augmented matrix to get RREF. We then find the values of the x, y, and z components and that is our solution.
+
+See also [[CramersRule.md]]
diff --git a/LinearAlgebra.md b/LinearAlgebra.md
@@ -67,3 +67,7 @@ Khan Unit 2:
- [[AmbientSpace.md]]
- [[Shear.md]]
- [[RightHandRule.md]]
+ - [[Duality.md]]
+ - [[CramersRule.md]]
+ - [[GaussianElimination.md]]
+ - [[EigenVector.md]]
diff --git a/Negation.md b/Negation.md
@@ -0,0 +1,8 @@
+:discrete:
+# Negation
+
+1.1.1
+
+## Notes
+
+**Definition:** Negation is the process of inverting the truthiness of a proposition.
diff --git a/Proposition.md b/Proposition.md
@@ -0,0 +1,8 @@
+:discrete:
+# Proposition
+
+Discrete 1.1
+
+## Notes
+
+**Definition:** A proposition is a statement that is either true or false.
diff --git a/Rank.md b/Rank.md
@@ -8,3 +8,5 @@ Khan
**Definition:** Rank, similar to [[Nullity.md]], is a way to describe the dimensionallity of the vector space generated by the columns of a matrix.
[[Nullity.md]] is the same thing except specifically referring to a matrix's null space.
+
+We call the rank 'full rank' when the rank is equivalent to the [[AmbientSpace.md]].
diff --git a/TexRef.md b/TexRef.md
@@ -18,3 +18,5 @@ List of TeX characters syntax I have had to look up.
\nmid - $\nmid$ this is the character to describe not divisible by. Weird syntax I know.
\not\equiv - $\not\equiv$ - This is the character describing not equivalent with the three lines horizontally.
+
+\oplus - $\oplus$ - This is the character for XOR which is a plus with a circle around it.
diff --git a/index.md b/index.md
@@ -21,6 +21,7 @@ This is the index for my main note classifications. I will maintain this as a ho
[[StatisticsAndProbability.md]]
[[LinuxStuff.md]]
[[LinearAlgebra.md]]
+[[DiscreteMath.md]]
[[Calculus.md]]
[[Algorithms.md]]
[[Physics.md]]
@@ -34,6 +35,7 @@ Stats + Prob
- [ ] https://en.wikipedia.org/wiki/Continuous-time_Markov_chain
Lin-alg
+ - [ ] Implement Stochastic Approach to Eigen vector/value calculation using grid.
- [ ] Inverse Matrix Calculations (do some practice problems)
- [ ] https://en.wikipedia.org/wiki/Invertible_matrix
- [ ] Laplace Expansion (define outside of determinant note)
