Some Important Terms
❑ Fibonacci Series
❑ Armstrong Number
❑ Palindrome
❑ Transpose Matrix
❑ Trace of a Matrix
❑ Norm of a Matrix
Fibonacci Series
A term in the series obtained by adding
previous two terms
.
Armstrong Number
An Armstrong number is a number that is equal to
the sum of its own digits raised to the power of the
number of digits it has.
Armstrong Number
An Armstrong number is a number that is equal to
the sum of its own digits raised to the power of the
number of digits it has.
Palindrome Number/String
A palindrome is a word or number that reads the same
forward and backward. In other words, when reversed, it
remains unchanged.
Palindrome Number/String
A palindrome is a word or number that reads the same
forward and backward. In other words, when reversed, it
remains unchanged.
Transpose Matrix
The transpose of a matrix is a new matrix formed by flipping the
rows and columns of the original matrix.
In other words, the rows of the original matrix become the columns
of the new matrix, and the columns become the rows.
Trace
The trace of a square matrix is the sum of the elements on its main
diagonal, which is the diagonal from the top left to the bottom
right of the matrix.
Norm
The norm of a matrix is a measure that describes the size or magnitude of
the matrix. There are various ways to calculate the norm of a matrix, such
as the Frobenius norm or the matrix p-norm.
For a 3 x 3 matrix:
The Frobenius norm of a matrix AA (denoted
1 23
as ∣∣A∣∣F∣∣A∣∣F) is calculated as the square
456
root of the sum of the squares of its elements:
789
For the given matrix:
∣∣A∣∣F = 12 + 22 + 32 +42 + 52 +62 + 72 +82 + 92
∣∣A∣∣F = 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81
∣∣A∣∣F = 285
∣∣A∣∣F ≈ 16.8819
Therefore, the Frobenius norm of the given 3x3 matrix is approximately 16.881916.8819.