Orthogonal Matrix

Hey guys, welcome again.

Today’s topic is Orthogonal Matrix.

So, let’s jump up to the topic.

Definition:

An Orthogonal matrix is a real square matrix, whose rows and columns are orthonormal vectors.

We can represent it as, A’A=AA’=I, where A’ is the transpose of A.

We can also say that-

If A’=A-1, i.e the transpose of the matrix is equal to the inverse then the matrix is called an orthogonal matrix.

Characteristics:

  1. An orthogonal matrix is a square matrix.
  2. If a matrix is orthogonal, then it is also invertible.
  3. An orthogonal matrix can be a Unitary Matrix.

Example:

Now let’s see an example of an orthogonal matrix.

So, we took the most general example to make it understandable to you.
Hope you all understand this.

If you have any question regarding this you can ask in the comment section.

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Snehasish Konger
Snehasish Konger

Hey, I'm Snehasish Konger, the guy behind this website.
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