docs: update linking

docs/mathematics/linear-algebra/eigenspaces.md

@@ -42,7 +42,7 @@ Furthermore it follows from the definition that any linear combination of eigenv
         A \mathbf{x} - \lambda \mathbf{x} = (A - \lambda I) \mathbf{x} = \mathbf{0},
     $$
 
-    which implies that $(A - \lambda I)$ is singular and $\det(A - \lambda I) = 0$ by [definition](../determinants/#properties-of-determinants). 
+    which implies that $(A - \lambda I)$ is singular and $\det(A - \lambda I) = 0$ by [definition](determinants.md#properties-of-determinants). 
 
 The eigenvalues $\lambda$ may thus be determined from the **characteristic polynomial** of degree $n$ that is obtained from $\det (A - \lambda I) = 0$. In particular, the eigenvalues are the roots of this polynomial.
 
@@ -110,7 +110,7 @@ The complex conjugate of an eigenvector of $A$ is also an eigenvector of $A$ wit
 
 ??? note "*Proof*:"
 
-    Let $A$ be a $n \times n$ matrix and let $\lambda_1, \dots, \lambda_n \in \mathbb{K}$ be the eigenvalues of $A$. It follows from the [fundamental theorem of algebra](../../number-theory/complex-numbers/#roots-of-polynomials) that 
+    Let $A$ be a $n \times n$ matrix and let $\lambda_1, \dots, \lambda_n \in \mathbb{K}$ be the eigenvalues of $A$. It follows from the [fundamental theorem of algebra](../number-theory/complex-numbers.md#roots-of-polynomials) that 
 
     $$
         \det (A - \lambda I) = (\lambda_1 - \lambda)(\lambda_2 - \lambda) \cdots (\lambda_n - \lambda),
@@ -182,7 +182,7 @@ for $k \in \mathbb{K}$.
 
 ### Hermitian case
 
-The following section is for the special case that a matrix is [Hermitian](../matrices/matrix-arithmatic/#hermitian-matrix). 
+The following section is for the special case that a matrix is [Hermitian](matrices/matrix-arithmetic.md#hermitian-matrix). 
 
 > *Theorem 7*: the eigenvalues of a Hermitian matrix are real.
 
@@ -264,4 +264,4 @@ The factorization $A = U T U^H$ is often referred to as the *Schur decomposition
 
 ??? note "*Proof*:"
 
-    Will be added later.
+    Will be added later.