commit 33978c4f87c919066cd1a299b31528e288e01d6e
parent 9cd83a2d266248a00400a845f8b3630634993887
Author: AndrewLockVI <andrewlaack1@gmail.com>
Date: Wed, 8 Jan 2025 13:56:20 -0600
Did daily notes stuff
Diffstat:
9 files changed, 70 insertions(+), 20 deletions(-)
diff --git a/DeepLearning.md b/DeepLearning.md
@@ -0,0 +1,15 @@
+
+:index: :dl: :ml:
+# Deep Learning
+
+This index tracks deep learning-related content. While much of my deep learning (DL) material is interspersed throughout my machine learning (ML) notes, separating them seems appropriate given the volume of ML notes I've accumulated.
+
+## Resources Studied
+
+1. **Deep Learning** - Goodfellow, Bengio, Courville
+
+## Links by Resource
+
+### **Deep Learning** - Goodfellow, Bengio, Courville
+
+
diff --git a/DirectSum.md b/DirectSum.md
@@ -1,8 +1,12 @@
:lin-alg:
# Direct Sum
-Ch 1
+**Source:** Linear Algebra Done Right
+
+**Chapter:** 1
## Notes
-**Definition:** A direct sum (denoted with a circle with a plus in it like xor) is a sum of two vector spaces that are disjoint except for the zero vector.
+**Definition:** A direct sum is a sum of two vector spaces that are disjoint except for the zero vector.
+
+This can also be stated as each element being writeable as a **unique** combination (sum) of vectors in the vector spaces. This notion leads to a good way to test this.
diff --git a/FiniteDimensional.md b/FiniteDimensional.md
@@ -0,0 +1,12 @@
+:linear-algebra:
+# Finite Dimensional
+
+**Source:** Linear Algebra Done Right
+
+**Chapter:** 2
+
+## Notes
+
+**Definition:** A vector space is finite dimensional if it contains a list of vectors that span the space.
+
+Finite dimensional is antithetical to infinite dimensional which is a vector space that does not contain a list of vectors that span the entire space. This can occur when we have a vector space that has an infinite number of coordinates, but since lists must be finite, we can't define a list of vectors that spans the entire space.
diff --git a/LinearAlgebra.md b/LinearAlgebra.md
@@ -14,10 +14,16 @@ Chapter 1:
- [Tuple](Tuple.md)
- [ComplexVectorSpace](ComplexVectorSpace.md)
- [Subspace](Subspace.md)
- - [SumOfVectorSpaces](SumOfVectorSpaces.md)
- - [DirectSum](DirectSum.md)
- [RealVectorSpace.md](RealVectorSpace.md)
- [Coordinate](Coordinate.md)
+ - [SumOfVectorSpaces](SumOfVectorSpaces.md)
+ - [DirectSum](DirectSum.md)
+
+Chapter 2:
+ - [LinearCombination](LinearCombination.md)
+ - [Span](Span.md)
+ - [FiniteDimensional](FiniteDimensional.md)
+ - [LinearIndependence](LinearIndependence.md)
Khan Academy:
diff --git a/LinearCombination.md b/LinearCombination.md
@@ -1,10 +1,12 @@
-:lin-alg: :discrete:
+:linear-algebra: :discrete:
# Linear Combination
-Khan
+**Source:** Linear Algera Done Right
+
+**Chapter:** 2
## Notes
-**Definition:** A linear combination is ca + db for any numbers c and d where a and b are vectors.
+### In Linear Algebra
-This is the most fundamental thing in lin algebra.
+**Definition:** A linear combination is ca + db for any scalars c and d where a and b are vectors.
diff --git a/LinearIndependence.md b/LinearIndependence.md
@@ -1,12 +1,16 @@
:lin-alg:
# Linear Independence
-Khan
+**Source:** Linear Algebra Done Right
+
+**Chapter:** 2
## Notes
**Definition:** Linear independence means that every column in a given matrix gives another degree of freedom.
+This can also be thought of as there only being one way to make every vector with linear combinations of vectors in the span.
+
Conversely, linear dependent vectors are vectors that are on the same line (or plane) as some other vector (or combination of vectors) thus not giving the matrix another degree of freedom.
Interesting thing; if you are in less dimensions than the number of vectors it is guaranteed their is linear dependence because you can't go beyond the current dimension.
diff --git a/Span.md b/Span.md
@@ -1,10 +1,12 @@
:lin-alg:
# Span
-Khan
+**Source:** Linear Algebra Done Right
+
+**Chapter:** 2
## Notes
-**Definition:** Span is a term that describes the space that can be represented in its entirety from a linear combination.
+**Definition:** The span of (v_1, ..., v_m) is the set of all linear combinations of (v_1, ..., v_m).
This may be all R^2, R^3, or some other space.
diff --git a/SumOfVectorSpaces.md b/SumOfVectorSpaces.md
@@ -1,8 +1,19 @@
:lin-alg:
# Sum of Vector Spaces
-Ch1
+**Source:** Linear Algebra Done Right
+
+**Chapter:** 1
## Notes
-**Definition:** The sum of two vector spaces is another vector space which is formed by all combinations of vectors in both spaces.
+**Definition:** The sum of two vector spaces is another vector space which is formed by all sums of vectors in both spaces (think combining each vector with every other vector).
+
+Note that the sum of vector spaces is not simply limited to two vector spaces and can be stated as follows for 3 vector spaces where V_1, V_2, V_3 are vector spaces as is S_1:
+
+S_1 = V_1 + V_2 + V_3
+
+### Other Information
+
+1. If U_1, U_2, U_3 are subspaces of V then so is U_1 + U_2 + U_3
+2. The smallest possible subspace that contains U_1, U_2, and U_3 is the sum of their vector spaces
diff --git a/index.md b/index.md
@@ -31,15 +31,10 @@ This is the index for my main note classifications. I will maintain this as a ho
[[Physics.md]]
[[Vocabulary.md]]
[[ReinforcementLearning.md]]
+[[DeepLearning.md]]
## Things to Learn More About
-Stats + Prob
-- [ ] ECDF (sort of like cdf)
-- [ ] Convolution (not NN)
-- [ ] https://en.wikipedia.org/wiki/Primality_test
-- [ ] https://en.wikipedia.org/wiki/Continuous-time_Markov_chain
-
Lin-alg
- [ ] Cofactor (define)
- [ ] Minors
@@ -53,5 +48,4 @@ ML
- [ ] Mamba
- [ ] Transformer
- [ ] KAN
-- [ ] Linear Regression statistical approach
- [ ] Boosting (XGBoost, AdaBoost, LightGBM, etc.)
