<aside> 💡 A matrix is a rectangular array of numbers, arranged in rows and columns.

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eg: $\begin{bmatrix} 1&2&3\\2&3&4\end{bmatrix}$ is a 2x3 matrix.

• A m$\times$n matrix has $m$ rows and $n$ columns.
• $(i,j)$-th entry of a matrix is the entry occurring in the $i$$^{th}$ row and $j$$^{th}$ column.

Square Matrices

<aside> 💡 A square matrix is a matrix in which the number of rows is same as the number of columns.

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eg: $\begin{bmatrix} 0.3&5&-7\\2.8&0&1\\0&-2.5&-1\end{bmatrix}$ is a 3$\times$3 matrix.

• The $i$$^{th}$ diagonal entry is the $(i,i)$$^{th}$ entry.
• The diagonal of a square matrix is the set of Diagonal entries.

Diagonal Matrices

<aside> 💡 A square matrix in which all entries except the diagonal are 0 is called a diagonal matrix.

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e.g.: $\begin{bmatrix} 1&0&0\\0&-3&0\\0&0&2.8\end{bmatrix}$ is a diagonal matrix.

Scalar Matrix

<aside> 💡 A diagonal matrix in which all the entries in the diagonal are equal is called a scalar matrix.

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e.g.: $\begin{bmatrix} -3&0&0\\0&-3&0\\0&0&-3\end{bmatrix}$ is a scalar matrix.

Identity Matrix

<aside> 💡 The scalar matrix with all diagonal entries 1 is called the identity matrix and is denoted by $I$.

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