Summary

Summary Linear Algebra, ISBN: 9781285463247 Linear Algebra (5082LIAL6Y)

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Course
Lineaire Algebra (5082LIAL6Y)

Institution
Universiteit Van Amsterdam (UvA)

Book
Linear Algebra

This is a summary of all lectures associated with the second half of the Linear Algebra course. I wrote this summary based on the lectures and the book. With this summary I finished the course with a 9.

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Summarized whole book? No
Which chapters are summarized? 4.1 , 4.2, 4.3, 4.4, 5.1, 5.2, 5.3, 5.4, 5.5, 7.3, 7.4,
Uploaded on September 12, 2021
Number of pages 9
Written in 2020/2021
Type Summary

linear algebra
university of amsterdam
artificial intelligence

Book Title:Linear Algebra

Author(s):David Poole

Edition:januari 2014
ISBN:9781285463247
Edition:1

Exam (elaborations)
Complete Solution Manual Linear Algebra A Modern Introduction 4th Edition David Poole
Summary
matrix multiplication easy visual method
Summary
linear algebra normalize

Institution
Universiteit van Amsterdam (UvA)
Education
Kunstmatige Intelligentie
Course
Lineaire Algebra (5082LIAL6Y)

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, scalar d is called A matrix ) if there is a nonzero vector (eigenvector ) Ax A X
'

a an eigenvalue of (n x n x such that =

the collection of all
eigenvectors corresponding to d
together with the zero vector, is called the
eigen space of d Ea
'
:
,

'

determinant of a 2×2 matrix A =
(da! %!) ,
det A =/ Al =
a. zazz a.zaz ,
-

[aag aa÷ aaa};] aa: I:} % I:3 % aa!!
A '
ll

'

determinant of a 3×3 matrix A = aeta -
- lat = a
-

a ta
.. , , ,
.. . ,

, ,

" t 't
( i, j) cofactor of A
Cig =L 1) A. ij
'
-
.
-
det

÷÷ '÷÷ '÷ I
-
check it cofactor is + or -

. .
.

-

the Laplace Expansion Theorem the determinant of an matrix A [a ;j] 22 det A C taizcizt tain Cin
'
: n x n =
,
where n = a . . .

;, ;,
n

E ( along i'throw
aijcij
= )
j= I
det A = a . C . t a C t ta C
zj 2J
. . .

n'j y nj nj
E (along j
'

aijcij
= th
i = I
column )

the determinant of a
triangular matrix det A
'
=
a
Azz ann
. . -

,,

-
A =
[a ;j ] is a square matrix a . if A has a zero row ( column ) det A = o

b . if B is obtained by interchanging two rows ( columns ) of A det B = -
det A

C .
if A has two identical rows ( columns ) det A = o

d . if B is obtained by multiplying a row ( column ) of A by K det B = K det (A )

e . if A B , C are identical except that the ith
,
row (column ) of C is the sum of the ith rows

(columns ) of A and B det C = det At det B

t . if B is obtained by adding a multiple of one row ( column ) of A to another row ( column )

det B = det A

'

E is an nxn
elementary matrix a . if E results from interchanging two rows of In det E = -
I

b . if E results from multiplying one row of In by K det E = K

C . if E results from adding a multiple of one row of In to another row det E =L

B is matrix and E is an matrix ( EB ) ( det E ) ( det
'

an n x n n x n
elementary det = B)

a square matrix is invertible iff det A t o
'

-

if A is an nxn matrix det ( KA ) = kndet A

if A and B are n x n matrices det ( AB ) =
( det A) (det B)
-

I
'
-
if A is invertible det ( A- ) = det A

for matrix det A aet A
any square
-
=

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Summary Linear Algebra, ISBN: 9781285463247 Linear Algebra (5082LIAL6Y)

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