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Matrix §

Identity Matrix §

Is a matrix where the diagonal is composed of all ones and the rest are zeros.

A property of this matrix is that if it is multiplied by any matrix , then

Square Matrix §

It’s a matrix where the number of rows and columns is the same.

Orthogonal matrix §

An orthogonal or orthonormal matrix is a real square matrix whose columns are orthonormal vectors. (backlink needed)

Where is the identity matrix.

Nonsingular matrix §

A matrix is called invertible or non-singular if there exists a matrix such that:

Theorem - Singular Matrix §

A square matrix is singular if and only if its determinant is zero.

Characteristics of a Singular Matrix:

• A singular matrix does not have an inverse.
• Cannot be inverted i.e doesn’t exists such that
• The rows or columns are linearly dependent

Determinant of a matrix §

It is a value that represent a certain geometric or algebraic property of the matrix.

For a 2 by 2 matrix the determinant is computed as the product of the elements on the main diagonal and the elements of the other diagonal:

Trace of a matrix §

The trace of a matrix is the sum of the elements on the main diagonal of A:

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• Orthogonal Matrix | Wikipedia