commit e6985e7bdd31911169ed36a4d86eacaef44f1e8d
parent e40014669d3f08c49c3b3dc60a9de707fe14a817
Author: Andrew <andrewlaack1@gmail.com>
Date: Thu, 1 Aug 2024 20:22:12 -0500
did stuff
Diffstat:
5 files changed, 32 insertions(+), 1 deletion(-)
diff --git a/IteratedExpectations.md b/IteratedExpectations.md
@@ -0,0 +1,8 @@
+:prob:
+# Iterated Expectations
+
+L12
+
+## Notes
+
+**Definition:** The law of iterated expectations states the expected value of a conditional expectation is the unconditional expectation.
diff --git a/LinearAlgebra.md b/LinearAlgebra.md
@@ -54,3 +54,4 @@ Khan Unit 2:
- [[StandardMatrix.md]]
- [[UnitVector.md]]
- [[Projection.md]]
+ - [[MatrixMultiplication.md]]
diff --git a/LinearTransformation.md b/LinearTransformation.md
@@ -60,6 +60,8 @@ T(x) = Ax
S(x) = Bx
Then:
-T(S(x)) = A(Bx)
+T(S(x)) = A(Bx) = ABx
+
+Compositions of matricies are associative, but not commutative.
With this definition it is intuitive that the standard matrix of the composition is A times B where A and B are the standard matricies of the L.T.s T and S.
diff --git a/MatrixMultiplication.md b/MatrixMultiplication.md
@@ -0,0 +1,18 @@
+:lin-alg:
+# Matrix Multiplication
+
+Khan U2
+
+## Notes
+
+**Definition:** The product of A and B is defined as AB where each column of AB is Axb_n where n is the number of the column.
+
+Idea:
+
+AB = [Ab_1 Ab_2 ... Ab_n]
+
+Note: To multiply two matricies the number of columns in the first matrix must be equal to the number of rows in the second matrix.
+
+AB is not equal to BA (in pretty much all cases). Often this is not even defined.
+
+See [[VectorMatrixMultipication.md]] for information about vector and matrix products.
diff --git a/StatisticsAndProbability.md b/StatisticsAndProbability.md
@@ -85,3 +85,5 @@ L10:
L11:
- [[Covariance.md]]
- [[CorrelationCoefficient.md]]
+L12:
+ - [[IteratedExpectations.md]]
