Matrix
A rectangular table of numbers with rows and columns. A matrix with m rows and n columns is called m by n.
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Analogy
A spreadsheet of numbers.
Example
[[1,2,3],[4,5,6]]It has 2 rows and 3 columns.Entry in row 2, column 3 is 6.Add matrices of the same size entrywise.
In practice
Matrices store data, describe equations, and represent transformations such as rotations.
Practice
Flashcards
- What size is the product of a 2 by 3 and a 3 by 4 matrix?2 by 4.
Questions people ask
When can two matrices be added?
Only when they have the same size, since you add matching entries. A 2 by 3 matrix cannot be added to a 3 by 2 matrix. Adding [[1,2],[3,4]] and [[5,6],[7,8]] gives [[6,8],[10,12]], by adding each position. Subtraction works the same way, and multiplying by a number scales every entry in the matrix.
What is the identity matrix?
A square matrix with ones down the diagonal and zeros elsewhere. Multiplying any matrix by it leaves it unchanged, just as multiplying a number by 1 does. The 2 by 2 identity is [[1,0],[0,1]]. It is written I, and inverses are defined using it.