All Flashcards
What is a matrix?
A rectangular array of numbers, symbols, or expressions arranged in rows and columns.
What are matrix dimensions?
The number of rows and columns in a matrix, expressed as n x m (rows x columns).
What is the dot product of two vectors?
The sum of the products of corresponding components of two vectors, resulting in a scalar.
Define matrix compatibility in multiplication.
For matrices A and B, the number of columns in A must equal the number of rows in B for multiplication to be possible.
Explain matrix multiplication compatibility.
The number of columns in the first matrix must equal the number of rows in the second matrix. If A is n x m and B is m x p, they are compatible.
Explain the dot product's geometric interpretation.
The dot product relates to the angle between two vectors; it measures how much the vectors point in the same direction.
Is matrix multiplication commutative? Explain.
No, matrix multiplication is generally not commutative. AB is not necessarily equal to BA.