Basic Matrix Algebra with Algorithms and Applications
ERRATA - March 2006
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right −→ left
left −→ right
two matrices −→ two distinct matrices
appears the −→ appears in the
more space between the second and third equations
+ + v32 −→ +v32
3 − 1 = 1 −→ 3 − 2 = 1
multiplication ... −→
multiplication
ofa vector
by Aand we can
−1 1 2
a11 a12
3 −1 2
combine them into
=
,
3 −1 2
2 0 4
a21 a22
−a21 + 3a22 = 3 −→ −a21 + 3a22 = 2
Matrix 1,4 entry: 3 −→ 2
? −→ .
are −→ is
+ i sin arg(z)+2kπ
= . . . −→ = |z|1/n cos arg(z)+2kπ
n
n
r > 0 −→ r ≥ 0
T
ab
a b
= −→
=
−b a
−b a
(f0 + f1 A −→ (f0 I + f1 A
12 + s2 + (−2)2 −→ 12 + 22 + (−2)2
y∗ T y∗ −→ y∗ y∗ T
Let ... . −→ Suppose a is a vector and let R be the matrix I − 2Pa .
Problems 3 and 4. −→ problems 5 and 6.
M [n+ 1,
i] −→ M [n, i + 1] 1
1
and
. The −→ and v2 =
. The
1
1
vT Au −→ vT Aw
In the next section, −→ In section 3.4,
see page 210.) −→ see page 209.)
· · · − f1 A + −f0 . −→ · · · − f1 A − f0 I.
· · · + −f0 Ak−n −→ −f0 Ak−n
the 22 entry −→ the 2, 2 entry
exactly −→ exactly a Fibonacci sequence with indices shifted by 1!
sequence
sequence
 8 −→ 


1 0 0
1 00

R =  0 c22 c23  −→ R =  0
Q
0 c2 c33
0
Q−1 CC −→ Q−1 CQ
. . . page 142, −→ page 144,
λt (x) −→ Λt (x)
λi (x) −→ Λi (x)
a(x − λ) . . . (x − λt ) −→ a(x − λ1 ) . . . (x − λt )
constant. −→ constant, where Λ(x) is DEFINED to be Λ1 (x) + · · · + Λt (x).
every polynomial This . . . ” −→ every polynomial. This . . . ’
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back
cover
page 110 −→ page 111
fi (A) −→ Λi (A)
or oscillates (a = −1) −→ or oscillates (a 6= 1)
eigenvector is w. −→ eigenvector w.
it doesn’t get there −→ it doesn’t get the
to late −→ too late
f2 = a12 , f3 = a13 −→ The f2 = a21 , f3 = a31
converges to 0. Therefore, this −→ converges. This
is used transmit −→ is used to transmit
µA (x) −→ µC (x)
“length” of A −→ “length” of C
C2 (A) = Cλ1 + Cλ2 −→ C2 (C) = Cλ1 + Cλ2
in part b ... −→ It appears in part b of Example 3.19 on page 169 and has eigenvalues
|M T v| −→ |M T v|2 ; λ|v| −→ λ|v|2
reducesthe −→ reduces the
det(A) . . . −→ det(A)
+ det(B)
= (−1)s+1 det(ms1 (A))
+(−1)t+1 det(mt1 (A)) as1 + (−1)s+1 det(ms1 (B)) + (−1)t+1 det(mt1 (B)) at1
l -16,-13,-3 (commas missing in four Vandermonde matrices)
l -1
The 2,4 entry of the matrix −2 −→ 2
l2
page 190) the −→ page 190 the
l4
· · · = x3 − 2x − 2. −→ · · · = x3 − 3x − 2 = (x + 1)2 (x − 2).
l6
page
 122 −→
 page 124

8
−8
2.2
2e  15  −→  15 
−24 
−24



1 0 0
1 0 0
 −→ 6. a. V −1 =  −3 2 −1 
1 −1
2.3
6. a. V −1 =  −3
2
2
2
2
1
1 −1 1
1
2
2
2
√
√
√ 2 −1 2
√
2.6
3. (−(3
3 + 4)/2,

−3/2 + 2 3) −→ (−(3 3 + 4)/2, −3/2 + 4 3)
1 0 0 −1 1
1 0 −1 1 0
2.7
2c.  0 1 0 −1 0  −→
0 1 −1 0 1
001 0 0
4.1
2. b −→ 2. c
10
1 0
2 −1
10
11
4.3
6a . . . −→ 7a
=
.
05
−3 1
1 2
11
01
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Mathematics
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