Special Types of Matrices

Diagonal matrix

A square matrix is a diagonal matrix if every entry off the main diagonal is zero. The diagonal entries themselves can be anything, including zero.

\begin{bmatrix} 4 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 7 \end{bmatrix}

Scalar matrix

A scalar matrix is a diagonal matrix where every diagonal entry is equal to the same number $k$ , a stricter version of "diagonal."

\begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix}

Identity matrix

The identity matrix, written $I$ , is the scalar matrix where that repeated diagonal value is specifically 1, the strictest of the three. It behaves like the number 1 does in ordinary multiplication: $AI = IA = A$ for any compatible matrix $A$ .

I = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}

So every identity matrix is a scalar matrix, every scalar matrix is a diagonal matrix, but not the other way around.

Special Types of Matrices

Diagonal matrix

A square matrix is a diagonal matrix if every entry off the main diagonal is zero. The diagonal entries themselves can be anything, including zero.

\begin{bmatrix} 4 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 7 \end{bmatrix}

Scalar matrix

A scalar matrix is a diagonal matrix where every diagonal entry is equal to the same number $k$ , a stricter version of "diagonal."

\begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix}

Identity matrix

I = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}

So every identity matrix is a scalar matrix, every scalar matrix is a diagonal matrix, but not the other way around.

Special Types of Matrices

Diagonal matrix

Scalar matrix

Identity matrix

Continue learning

Special Types of Matrices

Diagonal matrix

Scalar matrix

Identity matrix

Continue learning