commit 8b38a4fed496498a81ef7d29404085013fb2af61
parent c4d44e35e093c7f614d96c63a04e23e14c458540
Author: AndrewLockVI <andrewlaack1@gmail.com>
Date: Wed, 22 Jan 2025 08:28:41 -0600
Finished lin-alg notes for the day
Diffstat:
3 files changed, 15 insertions(+), 1 deletion(-)
diff --git a/definitions/InverseMatrix.md b/definitions/InverseMatrix.md
@@ -25,3 +25,8 @@ M' [ 1 0 0] = [1 0 0]
M' = [1 0 0]
[3 1 0]
[0 0 1]
+
+To solve for the inverse of a matrix we can create an inequality between A and I (or better would be an augmented matrix).
+We then make changes to both sides such that the left side of the inequality becomes the identity matrix. What was
+formerly the identity matrix is now the inverse matrix because those are the transformations required to convert from
+A to the identity matrix, hence A^-1 A = I.
diff --git a/definitions/LinearAlgebra.md b/definitions/LinearAlgebra.md
@@ -45,6 +45,15 @@ Lecture 2:
- [PermutationMatrix](PermutationMatrix.md)
- [InverseMatrix](InverseMatrix.md)
+Lecture 3:
+
+- [MatrixMultiplication](MatrixMultiplication.md)
+- [Singular](Singular.md)
+- [Invertible](Invertible.md)
+- [InverseMatrix](InverseMatrix.md)
+- [Determinant](Determinant.md)
+- [GaussianElimination](GaussianElimination.md)
+
Khan Academy:
Khan Unit 1 (mostly):
diff --git a/definitions/Singular.md b/definitions/Singular.md
@@ -8,6 +8,6 @@
**Definition:** For a matrix to be singular it must be a square matrix with a deteminant of zero.
-Given this definition, we also see this means the matrix must not be invertible.
+Given this definition, we also see this means the matrix must not be invertible. I think this is likely where the term 'singular' is derived from.
A matrix is singular if it is linearly dependent.
