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The Manga Guide to Linear Algebra by Ltd. Trend-Pro Co., Iroha Inoue, Shin Takahashi

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Vector Calculations 125
Vector Calculations
Even though vectors
have a few special
interpretations, they're a
just
n and n×1 matrices...
And they're
calculated in the
exact same way.
= (3 · 1 + 1 · 2) = 5
(10, 10) + (3, 6) = (10 + (3), 10 + (6)) = (7, 4)
(10, 10) (3, 6) = (10 3, 10 6) = (7, 4)
2(3, 1) = (2 · 3, 2 · 1) = (6, 2)
(3, 1)
Aition
10
10
7
4
3
6
+
10 + (3)
10 + (6)
= =
Subtraction
10
10
7
4
3
6
10 3
10 6
= =
Scalar multiplication
6
2
3
1
2
2 · 3
2 · 1
= =
Matrix Multiplication
3
1
6
2
3
1
1
2
3 · 1 3 · 2
1 · 1 1 · 2
(1, 2) = =
8
2
3
1
3
1
3
1
=
21
7
8 · 3 + (3) · 1
2 · 3 + 1 · 1
= = 7
Simple!
126 Chapter 5 Introduction to Vectors
Horizontal
vectors like this
one are caed
row vectors.
And vertical
vectors are
caed column
vectors.
Makes
sense.
We also ca the set of
a 1 matrices R
n
.
Sure,
why not...
R
n
aears a
lot in linear
algebra, so
make sure you
remember it.
No
problem.
When writing vectors by hand, we
usuay draw the leftmost line
double, like this.
A 2×1
vectors
A
3×1
vectors
A
1
vectors

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