Begyndelse på Typst-noter

01001 - Matematik 1a/Noter/Matrixalgebra og determinanter/Matrixalgebra og determinanter.typ

@@ -0,0 +1,54 @@
+#import "@local/dtu-template:0.5.1":*
+
+
+#show: dtu-math-assignment.with(
+  course: "01001",
+  course-name: "Mathematics 1a (Polytechnical Foundation)",
+  title: "Matrixalgebra og determinanter",
+  author: "Rasmus Rosendahl-Kaa (S255955)",
+  semester: "2025 Fall",
+)
+
+#set math.vec(delim: "[")
+#set math.mat(delim: "[")
+#set text(lang: "da")
+
+
+= Matrix
+$underline(underline(A))$ - en matrix\
+$underline(v)$ - en vektor
+
+Har en matrix:
+$
+underline(underline(A)) = mat(a_11,a_12,dots,a_(1n);dots.v,,,dots.v;a_(m 1),a_(m 2),dots,a_(m n)) space in FF ^(m times n)
+$
+
+*Søjlevektor:*\
+$ mat(a_11;dots.v;a_(m 1)) in FF^(m times 1) = FF^(m) $
+*Rækkevektor:*\
+$ mat(a_11,a_12,dots,a_(1 n)) in FF^(1 times n) $
+
+#definition(title: "Addition af vektorer")[
+To vektorer $underline(a) "og" underline(b)$: $underline(a)=mat(a_1;dots.v;a_m), underline(b)=mat(b_1;dots.v;b_m)$
+
+$ underline(a)+underline(b)=mat(a_1+b_1;dots.v;a_m+b_m) $
+]
+
+#definition(title: "Skalar af vektor")[
+Har en vektor $underline(a)$: $underline(a)=mat(a_1;dots.v;a_m)$ og en skalar $c in FF$:
+
+$ c dot underline(a) = mat(a_1 dot c;dots.v;a_m dot c) $
+]
+
+#definition(title: "Lineær kombination af vektor")[
+$underline(v_1),underline(v_2),dots,underline(v_n) in FF^m "og" c_1,c_2,dots,c_n in FF$
+$ c_1 dot underline(v_1) + c_2 dot underline(v_2) + dots + c_n dot underline(v_n) $
+Hedder en lineær kombination
+]
+
+= Lineær uafhængighed
+#definition(title: "7.1.1: Lineær uafhængighed")[
+Et sæt vektorer $(underline(v_1),underline(v_2),dots,underline(v_n)$ kaldes lineær uafhængige hvis og kun hvis ligningen:
+$ c_1 dot underline(v_1) + c_2 dot underline(v_2) + dots + c_n dot underline(v_n) $
+kun har én løsning: $c_1=c_2=dots=c_n=0$
+]

Diskret Mat/Graphs and the Cantor-Schröder-Bernstein theorem/Graphs and the Cantor-Schröder-Bernstein theorem.pdf

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 >>
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