Construction of a Matrix from Other Matrices (MATRIX-END MATRIX command)

You can use vector or rectangular matrices to construct a new matrix, separating row expressions by semicolons and components of row expressions by commas. If a column vector V _c has n elements and matrix M has the dimensions n × m, then {M; V _c} is an n × (m + 1) matrix. Similarly, if the row vector V _r has m elements and M is the same, then {M; V _r} is an (n + 1) × m matrix. In fact, you can paste together any number of matrices and vectors this way.

• All of the components of each column expression must have the same number of actual rows, and all of the row expressions must have the same number of actual columns.
• The distinction between row vectors and column vectors must be observed carefully when constructing matrices in this way, so that the components will fit together properly.
• Several of the matrix functions are also useful in constructing matrices; see in particular the MAKE, UNIFORM, and IDENT functions in Matrix Functions (MATRIX-END MATRIX command) .