m×pmatriisi

m×pmatriisi refers to a matrix with m rows and p columns. In linear algebra, a matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. The dimensions of a matrix are always specified as the number of rows first, followed by the number of columns. Therefore, an m×pmatriisi has m horizontal lines of entries and p vertical lines of entries.

The element in the i-th row and j-th column of an m×pmatriisi is often denoted by $a_{ij}$, where $1 \le i \le m$ and $1 \le j \le p$. The set of all m×p matrices with entries from a particular field (such as real numbers or complex numbers) forms a vector space. Operations such as matrix addition, scalar multiplication, and matrix multiplication are defined for matrices of compatible dimensions. For example, two matrices can be added only if they have the same dimensions, i.e., they are both m×p matrices.

Matrix multiplication is a fundamental operation in linear algebra. The product of an m×p matrix A and a p×n matrix B results in an m×n matrix C. This means that the number of columns in the first matrix must equal the number of rows in the second matrix for their product to be defined. m×pmatriisi are used in various applications, including solving systems of linear equations, representing linear transformations, and in fields like computer graphics, physics, and engineering.