Let $A,B\in {ℂ}^{n\times n}$ with $\mathrm{ind}\left(A\right)=k$ and $\mathrm{ind}\left(B\right)=s$ and let $L_B=B^2{B}^{†○}$. A new condition $\left(C_{s,\ast }\right)$: $R\left(A^k\right)\cap N\left({\left(B^s\right)}^{\ast }\right)=\left\{0\right\}$ and $R\left(B^s\right)\cap N\left({\left(A^k\right)}^{\ast }\right)=\left\{0\right\}$, is defined. Some new characterizations related to core-EP inverses are obtained when $B$ satisfies condition $\left(C_{s,\ast }\right)$. Explicit expressions of $B^{†○}$ and $B{B}^{†○}$ are also given. In addition, equivalent conditions, which guarantee that $B$ satisfies condition $\left(C_{s,\ast }\right)$, are investigated. We proved that $B$ satisfies condition $\left(C_{s,\ast }\right)$ if and only if $L_B$ has a fixed matrix form. As an application, upper bounds for the errors $\parallel B^{†○}-A^{†○}\parallel ∕\parallel A^{†○}\parallel$ and $\parallel B{B}^{†○}-A{A}^{†○}\parallel$ are studied.

让 $\mathrm{一种}，乙\in {ℂ}^{ñ\times ñ}$ 和 $\mathrm{印}（\mathrm{一种}）=ķ$ 和 $\mathrm{印}（乙）=s$ 然后让 ${\mathrm{大号}}_{乙}={乙}^{\mathrm{2个}}{乙}^{†○}$。新条件$（C_{s，\ast }）$： $\mathrm{[R}（{\mathrm{一种}}^{ķ}）\cap ñ（{（{乙}^s）}^{\ast }）=\left\{0\right\}$ 和 $\mathrm{[R}（{乙}^s）\cap ñ（{（{\mathrm{一种}}^{ķ}）}^{\ast }）=\left\{0\right\}$， 被定义为。在以下情况下获得了一些与核-EP逆相关的新特征：$乙$ 满足条件 $（C_{s，\ast }）$。的明确表达${乙}^{†○}$ 和 $乙{乙}^{†○}$还给出了。此外，等价条件可确保$乙$ 满足条件 $（C_{s，\ast }）$，正在调查中。我们证明了$乙$ 满足条件 $（C_{s，\ast }）$ 当且仅当 ${\mathrm{大号}}_{乙}$具有固定的矩阵形式。作为应用程序，错误的上限$\parallel {乙}^{†○}-{\mathrm{一种}}^{†○}\parallel ∕\parallel {\mathrm{一种}}^{†○}\parallel$ 和 $\parallel 乙{乙}^{†○}-\mathrm{一种}{\mathrm{一种}}^{†○}\parallel$ 被研究。