fix docs

Author: rasbt

docs/sources/CHANGELOG.md

@@ -21,7 +21,7 @@ The CHANGELOG for the current development version is available at
 - The `SequentialFeatureSelector` is now also compatible with Pandas DataFrames and uses DataFrame column-names for more interpretable feature subset reports. ([#379](https://github.com/rasbt/mlxtend/pull/379))
 - `ColumnSelector` now works with Pandas DataFrames columns. ([#378](https://github.com/rasbt/mlxtend/pull/378) by [Manuel Garrido](https://github.com/manugarri))
 - The `ExhaustiveFeatureSelector` estimator in `mlxtend.feature_selection` now is safely stoppable mid-process by control+c. ([#380](https://github.com/rasbt/mlxtend/pull/380))
-- Two new functions, `vectorspace_orthonormalization` and `vectorspace_dimensionality` were added to `mlxtend.math` to use the Gram-Schmidt process to convert an orthogonal vectorspace into orthonormal basis vectors and to compute the dimensionality of a vectorspace, respectively. ([#382](https://github.com/rasbt/mlxtend/pull/382))
+- Two new functions, `vectorspace_orthonormalization` and `vectorspace_dimensionality` were added to `mlxtend.math` to use the Gram-Schmidt process to convert a set of linearly independent vectors into a set of orthonormal basis vectors, and to compute the dimensionality of a vectorspace, respectively. ([#382](https://github.com/rasbt/mlxtend/pull/382))
 
 
 ##### Changes

docs/sources/user_guide/math/vectorspace_dimensionality.ipynb

@@ -32,7 +32,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Given a set of vectors, arranged as columns in a matrix, the `vectorspace_dimensionality` computes the number of dimensions (i.e., hyper-volume) that the vectorspace spans using the Gram-Schmidt process [1]. In particular, since the Gram-Schmidt process yields vectors that are zero or normalized to 1 (i.e., an orthonormal vectorset if the input was an orthogonal vectorset), the sum of the vector norms corresponds to the number of dimensions of a vectorset. "
+    "Given a set of vectors, arranged as columns in a matrix, the `vectorspace_dimensionality` computes the number of dimensions (i.e., hyper-volume) that the vectorspace spans using the Gram-Schmidt process [1]. In particular, since the Gram-Schmidt process yields vectors that are zero or normalized to 1 (i.e., an orthonormal vectorset if the input was a set of linearly independent vectors), the sum of the vector norms corresponds to the number of dimensions of a vectorset. "
    ]
   },
   {
@@ -203,7 +203,7 @@
       "\n",
       "- `ary` : array-like, shape=[num_vectors, num_vectors]\n",
       "\n",
-      "    An orthogonal set of vectors (arranged as columns in a matrix)\n",
+      "    A set of vectors (arranged as columns in a matrix)\n",
       "\n",
       "**Returns**\n",
       "\n",

docs/sources/user_guide/math/vectorspace_orthonormalization.ipynb

@@ -11,7 +11,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "A function that converts a set of orthogonal vectors to a set of orthonormal basis vectors."
+    "A function that converts a set of linearly independent vectors to a set of orthonormal basis vectors."
    ]
   },
   {
@@ -32,7 +32,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The `vectorspace_orthonormalization` converts a set of orthogonal vectors to a set of orthonormal basis vectors using the Gram-Schmidt process [1]. "
+    "The `vectorspace_orthonormalization` converts a set linearly independent vectors to a set of orthonormal basis vectors using the Gram-Schmidt process [1]. "
    ]
   },
   {
@@ -55,7 +55,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Note that to convert a set of orthogonal vectors into a set of orthonormal basis vectors, the `vectorspace_orthonormalization` function expects the vectors to be arranged as columns of a matrix (here: NumPy array). Please keep in mind that the `vectorspace_orthonormalization` function also works for non orthogonal vector sets; however, the resulting vectorset won't be orthonormal as a result. An easy way to check whether all vectors in the input set are orthogonal is to use the `numpy.linalg.det` (determinant) function."
+    "Note that to convert a set of linearly independent vectors into a set of orthonormal basis vectors, the `vectorspace_orthonormalization` function expects the vectors to be arranged as columns of a matrix (here: NumPy array). Please keep in mind that the `vectorspace_orthonormalization` function also works for non-linearly independent vector sets; however, the resulting vectorset won't be orthonormal as a result. An easy way to check whether all vectors in the input set are linearly independent is to use the `numpy.linalg.det` (determinant) function."
    ]
   },
   {
@@ -137,7 +137,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "However, in case of linear dependence(the second column is a linear combination of the first column in the example below), the vector elements of one of the dependent vectors will become zero. (For a pair of linear dependent vectors, the one with the larger column index will be the one that's zero-ed.)"
+    "However, in case of linear dependence (the second column is a linear combination of the first column in the example below), the vector elements of one of the dependent vectors will become zero. (For a pair of linear dependent vectors, the one with the larger column index will be the one that's zero-ed.)"
    ]
   },
   {
@@ -186,15 +186,15 @@
       "\n",
       "Transforms a set of column vectors to a orthonormal basis.\n",
       "\n",
-      "Given a set of orthogonal vectors, this functions converts such\n",
+      "Given a set of linearly independent vectors, this functions converts such\n",
       "column vectors, arranged in a matrix, into orthonormal basis\n",
       "vectors.\n",
       "\n",
       "**Parameters**\n",
       "\n",
       "- `ary` : array-like, shape=[num_vectors, num_vectors]\n",
       "\n",
-      "    An orthogonal set of vectors (arranged as columns in a matrix)\n",
+      "    A set of vectors (arranged as columns in a matrix)\n",
       "\n",
       "\n",
       "- `eps` : float (default: 1e-13)\n",