commit 2365f9ca67df8ac20649e57ba3996b0fd1c0dbe9
parent 980d6e91093338568009083b901d95698dbd3184
Author: Andrew <andrewlaack1@gmail.com>
Date: Mon, 5 Aug 2024 09:50:56 -0500
Took lin-alg notes
Diffstat:
5 files changed, 31 insertions(+), 4 deletions(-)
diff --git a/Bijective.md b/Bijective.md
@@ -1,4 +1,4 @@
-:calc:
+:calc: :lin-alg:
# Bijective
L2
diff --git a/Injective.md b/Injective.md
@@ -1,4 +1,4 @@
-:calc:
+:calc: :lin-alg:
# Injective
L2
diff --git a/InverseTransformation.md b/InverseTransformation.md
@@ -0,0 +1,24 @@
+:lin-alg:
+# Inverse Transformation (and matricies)
+
+Khan U2
+
+## Notes
+
+**Definition:** The inverse of a transformation is the transformation that undoes the original transformation for the entire domain codomain of the original transformation.
+
+This transformation must be [[Bijective.md]] otherwise there will be issues with mappings either there are outputs without inputs or there are outputs with multiple inputs.
+
+A transformation is invertible if and only if there exists an f^-1 such that f^-1 composed with f is I (identity function).
+
+(in the world of L.T.'s) Assume the standard matrix of f is A and the standard matrix of f^-1 is B. We then know:
+
+AB = I
+
+## Unique?
+
+Inverse functions are unique (there is only one).
+
+Let's assume they are not. We then find A(x) = B(x) for all x in R^n. This means A and B are the same function, but they are not. This is a contradiction.
+
+## Calculation
diff --git a/LinearAlgebra.md b/LinearAlgebra.md
@@ -55,4 +55,7 @@ Khan Unit 2:
- [[UnitVector.md]]
- [[Projection.md]]
- [[MatrixMultiplication.md]]
-
+ - [[InverseTransformation.md]]
+ - [[Surjective.md]]
+ - [[Injective.md]]
+ - [[Bijective.md]]
diff --git a/Surjective.md b/Surjective.md
@@ -1,4 +1,4 @@
-:calc:
+:calc: :lin-alg:
# Surjective
L2
