commit d5020aa881d8e183d03fa6122e0b4f5cdeefa0f8
parent 6563eae573abb1b7cfb265528bc3e4ee546ad3ee
Author: Andrew <andrewlaack1@gmail.com>
Date: Tue, 3 Sep 2024 15:29:06 -0500
Took notes from mml last time
Diffstat:
13 files changed, 114 insertions(+), 18 deletions(-)
diff --git a/Associative.md b/Associative.md
@@ -0,0 +1,12 @@
+:ml: :logic: :discrete:
+# Associative
+
+MML Ch 2.2
+
+## Notes
+
+**Definition:** Associativity of an operation means that regardless of the location of parenthesis the resulting computation is still the same assuming the order of values is also the same.
+
+Example:
+
+a + (b + c) = (a + b) + c
diff --git a/BasicVariables.md b/BasicVariables.md
@@ -0,0 +1,8 @@
+:lin-alg:
+# Basic Variables
+
+Ch 2.2
+
+## Notes
+
+**Definition:** Basic variables of a set of linear equations (or of a matrix) are variables that have a definite value which can be noted from the fact that they are the only 1 in the column when in RREF.
diff --git a/DiscreteRandomVariable.md b/DiscreteRandomVariable.md
@@ -5,4 +5,4 @@ Ch 2.1
## Notes
-**Definition:** A discrete random variable is a random variable upon finite or countably infite sets known as discrete sets.
+**Definition:** A discrete random variable is a random variable with an outcome space of finite or countably infinite size.
diff --git a/Distributive.md b/Distributive.md
@@ -0,0 +1,8 @@
+:ml: :discrete: :logic:
+# Distributive
+
+Ch 2.2
+
+## Notes
+
+**Definition:** Distributivity is a property of operators such that a(b+c) = ab + ac.
diff --git a/ElementaryTransformations.md b/ElementaryTransformations.md
@@ -0,0 +1,10 @@
+:lin-alg: :ml:
+# Elementary Transformations
+
+Ch 2.2
+
+## Notes
+
+**Definition:** Elementary transformations are transformations done to matricies that do not change the validity of the system of equations.
+
+These elementary transformations are what we use to solve systems of equations via gaussian elimination.
diff --git a/FreeVariables.md b/FreeVariables.md
@@ -0,0 +1,10 @@
+:lin-alg:
+# Free Variables
+
+Ch 2.2
+
+## Notes
+
+**Definition:** Free variables are variables in RREF that are not alone in their column.
+
+The existence of free variables means there are infinitely many solutions to a system of equations.
diff --git a/GeneralSolution.md b/GeneralSolution.md
@@ -0,0 +1,8 @@
+:lin-alg: :ml:
+# General Solution
+
+Ch 2.2
+
+## Notes
+
+**Definition:** A general solution to a system of linear equations is one that describes all possible solutions as combinations of each other.
diff --git a/MachineLearning.md b/MachineLearning.md
@@ -41,23 +41,23 @@ Math for Machine Learning:
Ch 2.2
- [MatrixMultiplication](MatrixMultiplication.md)
- [HadamardProduct](HadamardProduct.md)
- - IdentityMatrix
- - Associative
- - Distributive
- - Commutative
- - InverseTransformation
- - Transpose
- - SymmetricMatrix
- - LinearCombination
- - ParticularSolution
- - GeneralSolution
- - ElementaryTransformations
- - RowEchelonForm
- - BasicVariables
- - FreeVariables
- - ReducedRowEchelonForm
- - GaussianElimination
- - MinusOneTrick
+ - [IdentityMatrix](IdentityMatrix.md)
+ - [Associative](Associative.md)
+ - [Distributive](Distributive.md)
+ - [Commutative](Commutative.md)
+ - [InverseTransformation](InverseTransformation.md)
+ - [Transpose](Transpose.md)
+ - [SymmetricMatrix](SymmetricMatrix.md)
+ - [LinearCombination](LinearCombination.md)
+ - [ParticularSolution](ParticularSolution.md)
+ - [GeneralSolution](GeneralSolution.md)
+ - [ElementaryTransformations](ElementaryTransformations.md)
+ - [RowEchelonForm](RowEchelonForm.md)
+ - [BasicVariables](BasicVariables.md)
+ - [FreeVariables](FreeVariables.md)
+ - [ReducedRowEchelonForm](ReducedRowEchelonForm.md)
+ - [GaussianElimination](GaussianElimination.md)
+ - [MinusOneTrick](MinusOneTrick.md)
ML Categories:
diff --git a/MinusOneTrick.md b/MinusOneTrick.md
@@ -0,0 +1,10 @@
+:lin-alg:
+# Minus One Trick
+
+Ch 2.2
+
+## Notes
+
+**Definition:** The minus one trick is a method used to find general solutions to a system of equations by making a rectangular matrix a square matrix and adding -1 into each position along the diagnal that is not 1.
+
+By doing this we can then simply read out the general solution to the matrix instead of having to derive it.
diff --git a/ParticularSolution.md b/ParticularSolution.md
@@ -0,0 +1,8 @@
+:lin-alg: :ml:
+# Particular Solution
+
+Ch 2.2
+
+## Notes
+
+**Definition:** A particular solution to a set of linear equations are specific values that make all of the equalities of the system true.
diff --git a/RowEchelonForm.md b/RowEchelonForm.md
@@ -0,0 +1,10 @@
+:lin-alg:
+# Row Echelon Form
+
+Ch 2.2
+
+## Notes
+
+**Definition:** Row echelon form is a form such that all rows have more than or the same number of 0's starting from the left side as the row above them.
+
+In row echelon form there is no reduction of basic variables thus they don't need to be 1 like with RREF.
diff --git a/StatisticsAndProbability.md b/StatisticsAndProbability.md
@@ -50,6 +50,8 @@ Chapter 2.1:
- [RandomVariables](RandomVariables)
- [ProbabilityMassFunction](ProbabilityMassFunction.md)
- [DiscreteRandomVariable](DiscreteRandomVariable.md)
+ - Support (space of X)
+ - HypergeometricDistribution ()
---
diff --git a/SymmetricMatrix.md b/SymmetricMatrix.md
@@ -0,0 +1,10 @@
+:lin-alg: :ml:
+# Symmetric Matrix
+
+Ch 2.2
+
+## Notes
+
+**Definition:** A symmetric matrix is a matrix whereby A = A^T.
+
+When viewing a symmetric matrix we see that all values are mirrored across the diagonal that goes from top left to the bottom right of the matrix.
