diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleLinearOpsTensorAlgebra.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleLinearOpsTensorAlgebra.kt
index 82f63dd40..027fcf5d0 100644
--- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleLinearOpsTensorAlgebra.kt
+++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleLinearOpsTensorAlgebra.kt
@@ -14,8 +14,7 @@ public class DoubleLinearOpsTensorAlgebra :
 
     override fun DoubleTensor.det(): DoubleTensor = detLU()
 
-    override fun DoubleTensor.lu(): Pair<DoubleTensor, IntTensor> {
-
+    internal fun DoubleTensor.luForDet(forDet: Boolean = false): Pair<DoubleTensor, IntTensor> {
         checkSquareMatrix(shape)
 
         val luTensor = copy()
@@ -31,10 +30,22 @@ public class DoubleLinearOpsTensorAlgebra :
         )
 
         for ((lu, pivots) in luTensor.matrixSequence().zip(pivotsTensor.vectorSequence()))
-            luHelper(lu.as2D(), pivots.as1D(), m)
+            try {
+                luHelper(lu.as2D(), pivots.as1D(), m)
+            } catch (e: RuntimeException) {
+                if (forDet) {
+                    lu.as2D()[intArrayOf(0, 0)] = 0.0
+                } else {
+                    throw IllegalStateException("LUP decomposition can't be performed")
+                }
+            }
+
 
         return Pair(luTensor, pivotsTensor)
+    }
 
+    override fun DoubleTensor.lu(): Pair<DoubleTensor, IntTensor> {
+        return luForDet(false)
     }
 
     override fun luPivot(
@@ -66,11 +77,10 @@ public class DoubleLinearOpsTensorAlgebra :
 
     }
 
-    override fun DoubleTensor.cholesky(): DoubleTensor {
-        checkSymmetric(this)
+    public fun DoubleTensor.cholesky(epsilon: Double): DoubleTensor {
         checkSquareMatrix(shape)
-        //TODO("Andrei the det routine has bugs")
-        //checkPositiveDefinite(this)
+        checkPositiveDefinite(this)
+        //checkPositiveDefinite(this, epsilon)
 
         val n = shape.last()
         val lTensor = zeroesLike()
@@ -81,6 +91,8 @@ public class DoubleLinearOpsTensorAlgebra :
         return lTensor
     }
 
+    override fun DoubleTensor.cholesky(): DoubleTensor = cholesky(1e-6)
+
     override fun DoubleTensor.qr(): Pair<DoubleTensor, DoubleTensor> {
         checkSquareMatrix(shape)
         val qTensor = zeroesLike()
@@ -134,7 +146,7 @@ public class DoubleLinearOpsTensorAlgebra :
     }
 
     public fun DoubleTensor.detLU(): DoubleTensor {
-        val (luTensor, pivotsTensor) = lu()
+        val (luTensor, pivotsTensor) = luForDet(forDet = true)
         val n = shape.size
 
         val detTensorShape = IntArray(n - 1) { i -> shape[i] }
diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/checks.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/checks.kt
index 8dbf9eb81..45a71d1bc 100644
--- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/checks.kt
+++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/checks.kt
@@ -2,6 +2,7 @@ package space.kscience.kmath.tensors.core
 
 import space.kscience.kmath.tensors.TensorAlgebra
 import space.kscience.kmath.tensors.TensorStructure
+import kotlin.math.abs
 
 
 internal inline fun <T, TensorType : TensorStructure<T>,
@@ -63,9 +64,20 @@ internal inline fun DoubleTensorAlgebra.checkSymmetric(tensor: DoubleTensor, eps
         "Tensor is not symmetric about the last 2 dimensions at precision $epsilon"
     }
 
-internal inline fun DoubleLinearOpsTensorAlgebra.checkPositiveDefinite(tensor: DoubleTensor): Unit {
+internal inline fun DoubleLinearOpsTensorAlgebra.checkPositiveDefinite(
+    tensor: DoubleTensor, epsilon: Double = 1e-6): Unit {
+    checkSymmetric(tensor, epsilon)
     for( mat in tensor.matrixSequence())
         check(mat.asTensor().detLU().value() > 0.0){
             "Tensor contains matrices which are not positive definite ${mat.asTensor().detLU().value()}"
         }
+}
+
+internal inline fun DoubleLinearOpsTensorAlgebra.checkNonSingularMatrix(tensor: DoubleTensor): Unit {
+    for( mat in tensor.matrixSequence()) {
+        val detTensor = mat.asTensor().detLU()
+        check(!(detTensor.eq(detTensor.zeroesLike()))){
+            "Tensor contains matrices which are singular"
+        }
+    }
 }
\ No newline at end of file
diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/linutils.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/linutils.kt
index b3cfc1092..f2c9d8c76 100644
--- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/linutils.kt
+++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/linutils.kt
@@ -62,10 +62,10 @@ internal inline fun dotHelper(
 }
 
 internal inline fun luHelper(lu: MutableStructure2D<Double>, pivots: MutableStructure1D<Int>, m: Int) {
-    for (row in 0 until m) pivots[row] = row
+    for (row in 0..m) pivots[row] = row
 
     for (i in 0 until m) {
-        var maxVal = -1.0
+        var maxVal = 0.0
         var maxInd = i
 
         for (k in i until m) {
@@ -76,7 +76,9 @@ internal inline fun luHelper(lu: MutableStructure2D<Double>, pivots: MutableStru
             }
         }
 
-        //todo check singularity
+        if (abs(maxVal) < 1e-9) {
+            throw RuntimeException()
+        }
 
         if (maxInd != i) {
 
@@ -158,6 +160,9 @@ internal inline fun choleskyHelper(
 internal inline fun luMatrixDet(luTensor: MutableStructure2D<Double>, pivotsTensor: MutableStructure1D<Int>): Double {
     val lu = luTensor.as2D()
     val pivots = pivotsTensor.as1D()
+    if (lu[0, 0] == 0.0) {
+        return 0.0
+    }
     val m = lu.shape[0]
     val sign = if ((pivots[m] - m) % 2 == 0) 1.0 else -1.0
     return (0 until m).asSequence().map { lu[it, it] }.fold(sign) { left, right -> left * right }
diff --git a/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleLinearOpsAlgebra.kt b/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleLinearOpsAlgebra.kt
index 37caf88fe..75ff12355 100644
--- a/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleLinearOpsAlgebra.kt
+++ b/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleLinearOpsAlgebra.kt
@@ -36,6 +36,7 @@ class TestDoubleLinearOpsTensorAlgebra {
 
     @Test
     fun testDet() = DoubleLinearOpsTensorAlgebra {
+        val expectedValue = 0.019827417
         val m = fromArray(
             intArrayOf(3, 3), doubleArrayOf(
                 2.1843, 1.4391, -0.4845,
@@ -43,8 +44,20 @@ class TestDoubleLinearOpsTensorAlgebra {
                 -0.4845, 0.4055, 0.7519
             )
         )
-        println(m.det().value())
-        println(0.0197) //expected value
+
+        assertTrue { abs(m.det().value() - expectedValue) < 1e-5}
+    }
+
+    @Test
+    fun testDetSingle() = DoubleLinearOpsTensorAlgebra {
+        val expectedValue = 48.151623
+        val m = fromArray(
+            intArrayOf(1, 1), doubleArrayOf(
+                expectedValue
+            )
+        )
+
+        assertTrue { abs(m.det().value() - expectedValue) < 1e-5}
     }
 
     @Test