The present paper provides a procedure for constructing full-spark Parseval frames arising from the linear action of a 1-parameter group acting in ${\mathbb{R}}^n$. Precisely, given a square matrix A of order n, with real entries, we say that A induces the full spark frame property if the following conditions hold. There exists a vector v for which given any finite set $X\subset \mathbb{R}$ of cardinality n, the collection $\{\exp (xA)v:x\in X\}$ is a basis for ${\mathbb{R}}^n$. First, we show that if the spectrum of A is not a subset of the reals, then A does not induce the full spark frame property. Secondly, we establish that if the spectrum of A is a subset of the reals, then A induces the full spark frame property if and only if every eigenvalue of A has geometric multiplicity one. The proof of the latter fact gives a new algorithm for the construction of a class of full spark Parseval frames for ${\mathbb{R}}^n$.

本文提供了一种构建全火花 Parseval 框架的程序，该框架由作用于${\mathbb{R}}^n$. 准确地说，给定一个n阶的方阵A ，具有实数项，如果满足以下条件，我们说A会引发完整的火花框架属性。存在一个给定任意有限集的向量v$X\subset \mathbb{R}$基数n的集合$\{\mathrm{经验}(X\mathrm{一个})v：X\in X\}$是一个基础${\mathbb{R}}^n$. 首先，我们证明如果A的谱不是实数的子集，则A不会产生完整的火花框架属性。其次，我们确定如果A的谱是实数的一个子集，那么当且仅当A 的每个特征值都具有几何多重性时， A才会产生完整的火花框架属性。后一个事实的证明给出了一个新的算法来构造一类完整的火花 Parseval 帧${\mathbb{R}}^n$.