Matricies

Question 1

What is a matrix?

Answer 1

A 2D array of numbers arranged in rows and columns.

Question 2

What is a row in a matrix?

Answer 2

A horizontal group of elements.

Question 3

What is a column in a matrix?

Answer 3

A vertical group of elements.

Question 4

What is the size or dimension of a matrix?

Answer 4

The number of rows and columns, represented as m x n.

Question 5

What is a square matrix?

Answer 5

A matrix with the same number of rows and columns.

Question 6

What is a diagonal matrix?

Answer 6

A square matrix where all off-diagonal elements are zero.

Question 7

What is an identity matrix?

Answer 7

A diagonal matrix with 1s on the diagonal and 0s elsewhere.

Question 8

What is a zero matrix?

Answer 8

A matrix where all elements are 0.

Question 9

What is a symmetric matrix?

Answer 9

A matrix equal to its transpose.

Question 10

What is a transpose of a matrix?

Answer 10

A matrix obtained by swapping rows with columns.

Question 11

What is a sparse matrix?

Answer 11

A matrix where most elements are zero.

Question 12

What is a dense matrix?

Answer 12

A matrix with few or no zero elements.

Question 13

What is the time complexity to access an element in a matrix?

Answer 13

O(1) for direct access using indices.

Question 14

How is a matrix represented in code?

Answer 14

Typically as a list of lists or 2D array.

Question 15

What is matrix addition?

Answer 15

Adding corresponding elements of two matrices of the same size.

Question 16

What is matrix subtraction?

Answer 16

Subtracting corresponding elements of two matrices of the same size.

Question 17

What is scalar multiplication in a matrix?

Answer 17

Multiplying every element by a constant.

Question 18

What is matrix multiplication?

Answer 18

A row-by-column operation producing a new matrix.

Question 19

What is the condition for matrix multiplication?

Answer 19

The number of columns in the first matrix must equal the number of rows in the second.

Question 20

What is the time complexity of matrix multiplication?

Answer 20

O(n^3) for naïve method; faster algorithms like Strassen’s exist.

Question 21

What is a triangular matrix?

Answer 21

A matrix where all elements below or above the main diagonal are zero.

Question 22

What is a lower triangular matrix?

Answer 22

A matrix where all elements above the diagonal are zero.

Question 23

What is an upper triangular matrix?

Answer 23

A matrix where all elements below the diagonal are zero.

Question 24

What is a row-major order?

Answer 24

Matrix elements are stored row by row in memory.

Question 25

What is a column-major order?

Answer 25

Matrix elements are stored column by column in memory.

Question 26

What is the determinant of a matrix?

Answer 26

A scalar value that can be computed from a square matrix.

Question 27

What is the inverse of a matrix?

Answer 27

A matrix that, when multiplied with the original, gives the identity matrix.

Question 28

What is the rank of a matrix?

Answer 28

The maximum number of linearly independent rows or columns.

Question 29

What is a 2D array?

Answer 29

A data structure used to represent a matrix.

Question 30

What is a common use of matrices in programming?

Answer 30

Representing grids, images, graphs, and transformations.

Question 31

How do you iterate through a matrix?

Answer 31

Use nested loops over rows and columns.

Question 32

What is the space complexity of an m x n matrix?

Answer 32

O(m * n)

Question 33

What is a matrix rotation?

Answer 33

Rotating elements of a matrix 90, 180, or 270 degrees.

Question 34

How do you rotate a matrix 90 degrees clockwise?

Answer 34

Transpose and then reverse each row.

Question 35

What is a matrix diagonal traversal?

Answer 35

Accessing elements in a diagonal pattern from top-left to bottom-right.

Question 36

How do you flatten a matrix?

Answer 36

Convert it into a 1D array by row-wise or column-wise traversal.

Question 37

What is a matrix used for in graph representation?

Answer 37

Adjacency matrices represent connections between nodes.

Question 38

What is the diagonal of a matrix?

Answer 38

Elements where the row index equals the column index.

Question 39

What is matrix exponentiation?

Answer 39

Raising a matrix to a power, often used in dynamic programming.

Question 40

What is a submatrix?

Answer 40

A smaller matrix formed by selecting specific rows and columns.

Question 41

What is the trace of a matrix?

Answer 41

The sum of elements on the main diagonal.

Question 42

What is matrix slicing?

Answer 42

Extracting specific rows or columns from a matrix.

Question 43

Can matrices be sparse and symmetric?

Answer 43

Yes, a matrix can be both sparse and symmetric.

Question 44

What is the difference between a matrix and a dataframe?

Answer 44

A matrix is a pure numerical 2D structure; a dataframe can have labeled rows/columns and mixed data types.

Question 45

What is a block matrix?

Answer 45

A matrix partitioned into smaller submatrices.

Question 46

What is an element-wise operation on a matrix?

Answer 46

Operations applied independently to each element.

Question 47

What is the best data structure for storing sparse matrices?

Answer 47

Dictionary of keys (DOK) or compressed sparse row (CSR).

Question 48

What is a Toeplitz matrix?

Answer 48

A matrix where each descending diagonal from left to right is constant.