What a matrix is and the kinds of matrix you meet: square, zero, identity, diagonal and triangular. Then adding matrices, multiplying them and why the order of a product matters, and the transpose with symmetric and skew-symmetric matrices.
3 lessons, about 1 h 20 min3 simulations11 problems3 practice questionsPython in every lesson
Created by StemPy LabA matrix is a rectangular table of numbers. Its order is the number of rows by the number of columns. Two matrices are equal when they have the same order and the same entries in every place. You add matrices of the same order entry by entry, and you multiply a matrix by a number by multiplying every entry. Square, zero, identity, diagonal and triangular matrices are the special kinds.
The product exists when the number of columns of equals the number of rows of . Each entry of is a row of multiplied entry by entry with a column of and added. Multiplication is associative and distributes over addition, and the identity leaves a matrix unchanged. It is not commutative: and are usually different, and does not force or .
The transpose turns the rows of into columns. A matrix is symmetric when and skew-symmetric when , which forces zeros on its diagonal. The transpose of a product reverses the order: . Every square matrix is the sum of a symmetric part and a skew-symmetric part , in exactly one way.
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