commit c0c5be0f77a34dcbf1195c598254d21af8e07972
parent 8f4dbc6ae670f2238e79babbda0a1fcf57c3fd5d
Author: Andrew <andrewlaack1@gmail.com>
Date: Tue, 2 Jul 2024 21:39:30 -0500
took linear algebra notes
Diffstat:
11 files changed, 146 insertions(+), 1 deletion(-)
diff --git a/;:w b/;:w
@@ -0,0 +1,19 @@
+:lin-alg:
+# Vector Matrix Multiplication
+
+Reading
+
+## Notes
+
+**Definition:** Vector matrix multiplication can be performed by taking the combination of the first column of the matrix with the first top row of the vector and then repeating this throughout.
+
+As described above:
+
+```
+
+[2 1] [c] = [2c + 1d] = cv + dw
+[4 2] [d] [4c + 2d]
+
+
+```
+Where the vector [2,4] is v and [1,2] is w.
diff --git a/ColumnSpace.md b/ColumnSpace.md
@@ -0,0 +1,10 @@
+:lin-alg:
+# Column Space
+
+Lec 1
+
+## Notes
+
+**Definition:** The column space of a matrix the space that contains all combinations of the columns.
+
+In the case of a 3x2 (3 rows, 2 columns) matrix this, generally, is a plane. I say generally as if the two vectors are on the same line then they would be simply a line and not a plane.
diff --git a/DistanceCalculation.md b/DistanceCalculation.md
@@ -0,0 +1,21 @@
+:lin-alg:
+# Distance Calculation
+
+Reading
+
+## Notes
+
+**Definition:** Distance calculation in any dimension is defined as sqrt((x_1 - y_1)^2 + (x_2 - y_2)^2 ...)
+
+In the above definition x_1 is the first component of the first point (or vector), and y_1 is the first component of the second point (or vector). We then repeat this by subtracting them, squaring them and then summing all of them. Finally, we take the square root.
+
+In 1d this manifests as simply subtracting the first component of both as we square that and then take the square root of that.
+
+In 2d we have for the example (1,2) and (10, 12):
+
+ = sqrt((1 - 10)^2 + (2 - 12)^2)
+ = sqrt(81 + 100)
+ = sqrt(181)
+ = 13.453...
+
+We can expand this to higher dimensions, but you get the idea.
diff --git a/DotProduct.md b/DotProduct.md
@@ -1,4 +1,4 @@
-:cs331: :linear-algebra:
+:cs331: :lin-alg:
# Dot Product
CS331 + Linear Algebra
diff --git a/LinearAlgebra.md b/LinearAlgebra.md
@@ -0,0 +1,17 @@
+:index: :lin-alg:
+# Linear Algebra
+
+Linear algebra related links.
+
+The basis of linear algebra is solving systems of equations.
+
+## Links
+
+[[Matrix.md]]
+[[LinearEquations.md]]
+[[SystemsOfEquations.md]]
+[[LinearCombination.md]]
+[[ColumnSpace.md]]
+[[DistanceCalculation.md]]
+[[DotProduct.md]]
+[[VectorMatrixMultipication.md]]
diff --git a/LinearCombination.md b/LinearCombination.md
@@ -0,0 +1,10 @@
+:lin-alg:
+# Linear Combination
+
+Lec 1
+
+## Notes
+
+**Definition:** A linear combination is ca + db for any numbers c and d where a and b are vectors.
+
+This is the most fundamental thing in lin algebra.
diff --git a/LinearEquations.md b/LinearEquations.md
@@ -0,0 +1,10 @@
+:lin-alg:
+# Linear Equations
+
+Lec 1
+
+## Notes
+
+**Definition:** Linear equations are equations of the form y = mx+b where m and b are real coefficients.
+
+Simply, linear equations are any equation that results in a line when graphed.
diff --git a/Matrix.md b/Matrix.md
@@ -0,0 +1,18 @@
+:lin-alg:
+# Matrix
+
+L1
+
+## Notes
+
+**Definition** A matrix is a 2d grid of numerical values.
+
+Matricies can be used to describe systems of equations as follows:
+
+4x - 2y = 10
+-2x + y = 2
+
+[4 -2] [x] = [0]
+[-2 1] [y] = [3]
+
+This is the form because we distribute x on the first column and y on the second column.
diff --git a/SystemsOfEquations.md b/SystemsOfEquations.md
@@ -0,0 +1,8 @@
+:lin-alg:
+# Systems of Equations
+
+Lec 1
+
+## Notes
+
+**Defintition:** Systems of equations are sets of equations that are to be solved together.
diff --git a/VectorMatrixMultipication.md b/VectorMatrixMultipication.md
@@ -0,0 +1,31 @@
+:lin-alg:
+# Vector Matrix Multiplication
+
+Reading
+
+## Notes
+
+**Definition:** Vector matrix multiplication can be performed by taking the combination of the first column of the matrix with the first top row of the vector and then repeating this throughout.
+
+As described above:
+
+```
+
+[2 1] [c] = [2c + 1d] = cv + dw
+[4 2] [d] [4c + 2d]
+
+
+```
+
+Where the vector [2,4] is v and [1,2]
+
+
+Let's do another one.
+
+```
+
+[2 4 8] [8] = [16 + 36 + 32] = [ 84]
+[8 9 0] [9] [64 + 81 + 0 ] [145]
+[7 8 1] [4] [56 + 72 + 4 ] [132]
+
+```
diff --git a/index.md b/index.md
@@ -19,6 +19,7 @@ This is the index for my main note classifications. I will maintain this as a ho
[[Statistics.md]]
[[LinuxStuff.md]]
[[ModelNotes.md]]
+[[LinearAlgebra.md]]
## Technology Books to Read
