Summary Linear Algebra, ISBN: 9781285463247 Linear Algebra (5082LIAL6Y)
61 views 1 purchase
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.
Solutions Manual for Linear Algebra A Modern Introduction 4th Edition by David Poole 2024 . All Chapters A+
Complete Solution Manual Linear Algebra A Modern Introduction 4th Edition David Poole
matrix multiplication easy visual method
All for this textbook (6)
Written for
Universiteit van Amsterdam (UvA)
Kunstmatige Intelligentie
Lineaire Algebra (5082LIAL6Y)
All documents for this subject (2)
Seller
Follow
camilleniessink1
Reviews received
Content preview
, 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
-
=
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller camilleniessink1. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $9.20. You're not tied to anything after your purchase.
