aboutsummaryrefslogtreecommitdiff
path: root/li/05_linear_span
diff options
context:
space:
mode:
Diffstat (limited to 'li/05_linear_span')
-rw-r--r--li/05_linear_span17
1 files changed, 17 insertions, 0 deletions
diff --git a/li/05_linear_span b/li/05_linear_span
new file mode 100644
index 0000000..ed5fdf2
--- /dev/null
+++ b/li/05_linear_span
@@ -0,0 +1,17 @@
+ Linear Independence and Linear Span
+Solution set for Ax=0, Ax=B, and the dimension of null space/rank of a
+matrix.
+
+Def. linear independence over vector space (V, +, *)
+Let v = {v1, ..., vk} be vectors in V. We say v is linearly independent
+iff whenever a1v1 + a2v2 + ... akvk = 0, a1 = a2 = ... = ak = 0.
+
+Where v_i in v in R^n, we can find linear independence by writing it as
+
+[ v1 | v2 | ... | vk ][a1 a2 ... ak]^T = 0
+
+Prove: basis of a vector space has the same dimension regardless of the
+vectors.
+
+Def basis: a linearly independent set of vectors which spans a vector
+space.