Define the shape of a matrix
In the context of matrices in linear algebra, the shape of a matrix refers to its dimensions or size
In the context of matrices in linear algebra, the shape of a matrix refers to its dimensions or size. It describes the number of rows and columns the matrix contains. Typically, the shape of a matrix is denoted as “m x n,” where “m” represents the number of rows and “n” represents the number of columns.
For example, if a matrix has 3 rows and 2 columns, we say that it is a 3 x 2 matrix. This can be visually represented as follows:
[ a11 a12 ]
[ a21 a22 ]
[ a31 a32 ]
Here, the matrix has 3 rows and 2 columns. Each entry, represented as aij, corresponds to a specific element in the matrix. In this case, a11 represents the element in the first row, first column, a12 represents the element in the first row, second column, and so on.
The shape of a matrix is an important characteristic as it determines certain operations that can be performed on it. For example, two matrices can only be added or subtracted if they have the same shape (same number of rows and columns). Similarly, matrix multiplication is only defined when the number of columns in the first matrix matches the number of rows in the second matrix.
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