Lecture 1 - Linear algebra

Question 1

Square matrix

Answer 1

n columns and n rows

Question 2

Diagonal matrix

Answer 2

square matrix with non-zero elements only on main diagonal

Question 3

Band matrix

Answer 3

Non-zero elements only on main diagonal and few neighboring diagonals

Question 4

Triangular matrix

Answer 4

square matrix with non-zero elements only below or above the main diagonal , main diagonal included

Question 5

Identity matrix I

Answer 5

diagonal matrix with elements equal to 1

Question 6

Symmetric matrix

Answer 6

square matrix where a[i][j]=a[j][i]

Question 7

Sparse matrices

Answer 7

Many problems are based on matrices, which contains at most 1% of non-zero elements. It’s more efficient and faster if we store them in the SPARSE format.
e.g.: compressed row storage CRS

Question 8

Arithmetic

Answer 8

Addition
Subtraction
Multiplication -> NON-commutative
Dot product

Question 9

Transposition

At or A’

Answer 9

swapping rows and columns in such way that after it a[i][j] ==a[j][i]
(AB)t=BtAt

Question 10

Fractal

Answer 10

Set with following features:

• > self-similarity - similar patterns at increasingly small scales
• > fine or detailed structure at arbitrarily small scales
• > is not easily described in traditional Euclidean geometric language
• > simple and recursive definitions

Question 11

Benoit Mandelbrote

Answer 11

MANDELBROT fractal:

• > for each point at the complex plane
• > recurrence formula z(0)=0, z(i+1) = z(i)^2+p
• > The Mandelbrot set consist of the points that do not converge to the infinity

Question 12

Norm of a vector

Answer 12

it’s length

Question 13

Orthogonal vectors

Answer 13

Dot product = 0 <=> at * b = 0