Matrices and Vectors Vocab

From Adjectives at home lesson

Square Matrix

An m × n matrix is square if m = n

Diagonal of a Matrix

The collection of (i,i) entries

Upper Triangular Matrix

A matrix is upper triangular if every entry below the diagonal is zero (aij = 0 for i > j)

Lower Triangular Matrix

A matrix is lower triangular if every entry above the diagonal is zero (aij = 0 for i < j)

Diagonal Matrix

A matrix is diagonal if every nondiagonal entry is zero (aij = 0 for i ≠ j)

diag(d1, …, dn)

The n × n diagonal matrix with diagonal d1, …, dn

Zero Matrix

A matrix that is full of zeros

Zero Vector

A vector that is full of zeros

Nonzero Matrix

A matrix or vector is nonzero if at least one entry is nonzero

Identity Matrix In

The n × n identity matrix In has ones on the diagonal and zeros elsewhere

First Pivot Column

The first nonzero column of a matrix

Rank One Matrix

A matrix is rank one if every column is a multiple of the first pivot column

Blank Entries Convention

Blank entries in a matrix are understood to equal zero