**Life cycle diagram** Constructs a diagram of
the life cycle specified by a projection matrix.

**Basic analysis. **Enters several array formulas that together compute
some important properties of a population projection matrix -- such as the
generation times and eigenvalues and eigenvectors associated to the dominant
eigenvalue (giving the finite rate of increase, and stable age structure and
reproductive value).

**Finite rate of increase. **Enters formula for the dominant eigenvalue of
a population projection matrix.

**Age distribution****. **Enters an array formula for the right
eigenvector associated to the dominant eigenvalue of a population projection
matrix.

**Reproductive value****. **Enters an array formula for the left
eigenvector associated to the dominant eigenvalue of a population projection
matrix.

**Matrix sensitivity****. **Enters an array formula for the sensitivity
of the dominant eigenvalue of a population projection matrix to small changes in
the elements of the matrix.

**Matrix to row vector.** Inserts a row of formulas pointing to the
entries in a matrix.

**Matrix to column vector.** Inserts a column of formulas pointing to the
entries in a matrix.

**Matrix projection. **Iterates a population projection matrix for a
certain number of steps. Similar to Numerical
projection but requires a fixed projection matrix and a state vector
as input.

**Eigenanalysis. **Enters an array formula for the eigenvalues (real and
imaginary parts) and associated eigenvectors of a square matrix.

**LU decomposition****. **Enters an array formula that returns the
lower/upper decomposition of a square matrix.

**Cholesky** **decomposition****. **Enters an array formula that
returns the Cholesky decomposition of a positive definite matrix.

**QR decomposition. **Enters an array formula that returns the returns the
QR decomposition of a matrix with rows >= columns.

**Singular value decomposition. **Enters an array formula that returns the
singular value decomposition of a matrix.