notes

commit 3bf9866d6417d86f425ed82d8fcbf6684f74ea33
parent c0c5be0f77a34dcbf1195c598254d21af8e07972
Author: Andrew <andrewlaack1@gmail.com>
Date:   Wed,  3 Jul 2024 15:45:14 -0500

Took some linear algebra notes

Diffstat:
A
Invertible.md
 | 
8
++++++++
M
LinearAlgebra.md
 | 
4
++++
A
LinearIndependence.md
 | 
19
+++++++++++++++++++
A
Span.md
 | 
10
++++++++++
A
UnitVector.md
 | 
8
++++++++

5 files changed, 49 insertions(+), 0 deletions(-)
diff --git a/Invertible.md b/Invertible.md
@@ -0,0 +1,8 @@
+:lin-alg:
+# Invertible (Matrix)
+
+Reading
+
+## Notes
+
+**Definition:** For a matrix A to be invertible there must be another matrix B such that A * B = I where I is the identity matrix.
diff --git a/LinearAlgebra.md b/LinearAlgebra.md
@@ -15,3 +15,7 @@ The basis of linear algebra is solving systems of equations.
 [[DistanceCalculation.md]]
 [[DotProduct.md]]
 [[VectorMatrixMultipication.md]]
+[[Invertible.md]]
+[[UnitVector.md]]
+[[Span.md]]
+[[LinearIndependence.md]]
diff --git a/LinearIndependence.md b/LinearIndependence.md
@@ -0,0 +1,19 @@
+:lin-alg:
+# Linear Independence
+
+Khan
+
+## Notes
+
+**Definition:** Linear independence means that every column in a given matrix gives another degree of freedom. 
+
+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. 
+
+Ie.
+
+[2 7 10]
+[3 8  1]
+
+Given that [2,3] and [7,8] consumes all of R^2, we know there are no degrees of freedom provided by [10,1] despite it not being on either of the lines created by the first two columns.
diff --git a/Span.md b/Span.md
@@ -0,0 +1,10 @@
+:lin-alg:
+# Span
+
+Khan
+
+## Notes
+
+**Definition:** Span is a term that describes the space that can be represented in its entirety from a linear combination.
+
+This may be all R^2, R^3, or some other space.
diff --git a/UnitVector.md b/UnitVector.md
@@ -0,0 +1,8 @@
+:lin-alg:
+# Unit Vector
+
+Reading
+
+## Notes
+
+**Definition:** A unit vector is any vector with length of 1.