Classify each of the following matrices according as it is (a) real, (b) symmetric, (c) skew-symmetric, (d) Hermitian, or (e) skew-hermitian, and iden

illusiia

illusiia

Answered question

2020-11-08

Classify each of the following matrices according as it is (a) real, (b) symmetric, (c) skew-symmetric, (d) Hermitian, or (e) skew-hermitian, and identify its principal and secondary diagonals.
[10i024ii4+i3]
[70402104105]

Answer & Explanation

izboknil3

izboknil3

Skilled2020-11-09Added 99 answers

Step 1
Real matrix A real matrix is a matrix whose elements consist entirely of real numbers.
Symmetric matrix A symmetric matrix is a square matrix that is equal to its transpose.
AT=A
Skew symmetric matrix A matrix can be skew symmetric only if it is square. If the transpose of a matrix is equal to the negative of itself, the matrix is said to be skew symmetric.
AT=A
Step 2
Hermitian matrices Hermitian matrices can be understood as the complex extension of real symmetric matrices.
Aθ=A
skew-Hermitian matrices skew-Hermitian matrices can be understood as the complex versions of real skew-symmetric matrices, or as the matrix analogue of the purely imaginary numbers.
Aθ=A
Step 3
(1) Consider the provided question,
Let A=[10i024ii4+i3]
Now, check the given matrix for the above condition.
check for Hermitian matrix,
A¯=[10i024+ii4i3] Now Aθ=A¯T=[10i024ii4+i3]
Therefore , Aθ=A
So, it is satisfy the Hermitian matrix,
Step 4
The principal diagonal element of the matrix,
[10i024ii4+i3] is [123]
The Secondary diagonal element of the matrix,
[10i024ii4+i3] is [i2i]
Step 5
(2) Consider the provided question,
Let A=[70402104105]
Now, check the given matrix for the above condition.
check for symmetric matrix,
AT=[70402104105] therefore , AT=A
So, it is satisfy the symmetric matrix,
Step 6
The principal diagonal element of the matrix,
[70402104105] is [725]
The Secondary diagonal element of the matrix,
[70402104105] is [424]

Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-22Added 2605 answers

Answer is given below (on video)

Jeffrey Jordon

Jeffrey Jordon

Expert2022-08-23Added 2605 answers

Answer is given below (on video)

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