Chapter 1
1.1
scalar
parallelogram transpose perpendicular whole number
This big view, taking all the combinations of v and w, is linear algebra at work.
In 3D space, in typical situation
The combinations cu fill a line.
The combinations cu + dv fill a plane.
The combinations cu + dv +ew fill three-dementional space.
REVIEW:
1. A vector in 2D space has 2 components v1 and v2.
2. v+w=(v1+w1, v2+w2) and cv=(cv1, cv2).
3. a linear combination of 3 vectors u and v and w is cu+dv+ew;
4. take all linear combinations of u, or u&v, or u&v&w, in 3D space, these combinations typically fill a line, the a plane, then the whole space R3.
1.2 Length and Dot Product
dot product (inner product) right angle see-saw moment vector perpendicular
点乘的应用和意义: 力矩(力向量 与 力臂向量 的点乘为 合力矩); 收支平衡(产品数量向量 和 产品买/卖向量 的点乘为 总收入).
A zero product measns that "the book balance".
Length = norm(v) = √(v·v).
unit vector: u = v / |v|.
standard unit vector: i, j, k (axis).
cosine formula: v·w = |v|*|w|*cosθ
Schwarz formula:
triangle inequality formula:
geometric mean <= arithmetic mean:
REVIEW:
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4.
5.
