Linear Algebra with Sage

<Vectors>

Made by SKKU Linear Algebra Lab (2011)

Define a vector @@ \textbf{v}_1 @@(벡터 @@ \textbf{v}_1 @@생성 및 확인)

v1 = vector([1,2]); v1

(1, 2)

Find 0.5 @@\textbf{v}_1@@ (스칼라 배)

print 0.5*v1 show(plot(v1, color="blue")+plot(1/2*v1, color="green"), aspect_ratio=1)

(0.5, 1)

Define a vector @@\textbf{v}_2@@ (벡터 @@\textbf{v}_2@@ 생성 및 확인)

v2=vector([3,1]); v2

(3, 1)

Find @@\textbf{v}_1 + \textbf{v}_2@@ (두 벡터의 합)

print v1+v2 show(plot(v1, color="blue")+plot(v2, color="red")+plot(v1+v2, color="purple"), aspect_ratio=1)

(4, 3)

Find @@\textbf{v}_1 - \textbf{v}_2@@ (두 벡터의 차)

print v1-v2 show(plot(v1, color="blue")+plot(v2, color="red")+plot(v1-v2, color="purple"), aspect_ratio=1)

(-2, 1)

Find @@\textbf{v}_1 \cdot \textbf{v}_2@@ (두 벡터의 내적)

v1.dot_product(v2)

5

Find @@ || \textbf{v}_1 ||@@ (벡터의 크기)

v1.norm()

sqrt(5)